Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

A.A. Johansen; D. Anselmi; D.Z. Freedman; M.T. Grisaru

REVIEW

Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

D. Anselmi, D.Z. Freedman, M.T. Grisaru, A.A. Johansen

High Energy Physics - Theory · Submitted 7 Aug 1997 · 28 references

Pith's verdict: A solid, checkable 1997 paper: the a-flow result in the conformal window is the real contribution, and the derivation holds up under scrutiny.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/9708042 (version 1)

Pith IDRFEWUBMV, Pith's permanent record of this paper and its review

CitationA.A. Johansen, D. Anselmi, D.Z. Freedman, M.T. Grisaru. "Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories." arXiv:hep-th/9708042 (1997). https://pith.science/paper/RFEWUBMV

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to know: this paper gives explicit nonperturbative formulas for the flows of the flavor central charge b, the stress-tensor charge c, and the Euler coefficient a in N=1 SU(Nc) SQCD, and the a result is the one that matters. Eq. (4.23) plus the free-field UV values gives a_IR - a_UV = (Nc^2/48)(9 - 2x - 27/x^2) with x = Nf/Nc, strictly negative on the open window 3/2 < x < 3. That is a genuine strong-coupling test of the four-dimensional a-theorem, and it is the reason people still cite this paper. The c flow changes sign across the window, which the authors report honestly rather than burying, and they draw the correct conclusion that there is no supersymmetric c-theorem for c. Good, unsentimental reporting of a negative result alongside the positive one. The machinery is the interesting part: 't Hooft matching for the anomaly-free current S_mu in eq. (2.4), combined with the NSVZ beta function to fix gamma_IR. That S_mu is genuinely anomaly-free and scale-independent is the independent input that keeps the argument from being circular, and the two-loop coefficient identities in eq. (4.17) are a real cross-check, not decoration. Where I would push: the step that identifies the external trace-anomaly coefficient with the central function is argued by analogy and by citation to the authors' own ref. [8], not derived here from first principles. It is the framework the paper is built on, and it is plausible, but it is the softest joint. The boundary case Nf = 3Nc gives equality rather than strict inequality, so the 'always' in the abstract means 'on the open window'. Section 5's positivity conditions are explicitly speculative and the authors say so; treat that part as a conversation starter, not a result. The Seiberg inputs are cited published work, so I would not call them a flaw. Who should read it: anyone working on anomaly matching, conformal windows, or the a-theorem, and anyone who wants a clean worked example of extracting fixed-point data from UV triangle graphs. It deserves a serious referee and it has had one, historically. Engage with it.

Referee report

Significance

If correct, this is a substantial contribution: it gives the first nonperturbative, closed-form expressions for the flow of the Euler anomaly coefficient in a strongly coupled four-dimensional theory, and it converts the a-theorem conjecture into a falsifiable statement within a well-defined class of theories. The paper is careful to cross-check its general formulas against known two-loop results (Eqs. (4.16), (4.17)) and against the free-field UV values of Eq. (4.4), and it explicitly separates what is proved from what is conjectured. The explicit infrared values in Eq. (4.23) are a concrete, checkable prediction. The paper also correctly notes that its flows do not constitute new tests of Seiberg duality, since the S_mu anomalies are matched by construction; that honesty is a strength.

Major objections (3)

[§4, Eqs. (4.9)-(4.15) and Eq. (4.23)] The derivation of the IR values c_IR and a_IR in Eq. (4.23) rests on the coefficient identities collected in Eq. (4.17), which in turn depend on the UV values k_UV, k1_UV, k2_UV, k3_UV quoted in Eq. (4.14). The entry for k2_UV in Eq. (4.14) is written as 'k 2U V ≡ − 916NχNcNf', which as typeset is dimensionally and numerically inconsistent with the neighboring entries and with the identity in Eq. (4.17). The reader can reconstruct the intended value, but the manuscript should state it unambiguously and show at least one intermediate step in the verification of Eq. (4.17), since that identity is load-bearing for the central claim a_UV - a_IR > 0.
[§4, Eq. (4.15) and §5, Eq. (5.1)] The decomposition of c and a into UV values plus terms proportional to (gamma - gamma_IR), gamma_IR, and h in Eq. (4.15) is presented without derivation of the coefficients 5/6 and 1/2 that multiply (gamma - gamma_IR)k and gamma_IR k_UV. These coefficients are exactly what determines the relative size of the c and a flows, and hence the sign structure that the paper's conclusion depends on. A short derivation, or a pointer to the specific triangle-graph computation that fixes them, would make the central claim independently checkable rather than merely plausible.
[§5, Eq. (5.2) and the surrounding discussion] The extension of the a-flow result to the case where quark masses are introduced or the Higgs mechanism is used, Eq. (5.2), is stated without derivation and without specifying the range of N'_c and N'_f for which the IR theory is assumed to be in the conformal window. The claim that a_IR - a_UV < 0 holds 'in this more general situation' is a nontrivial extension of the main result and should either be derived or explicitly flagged as a conjecture supported by the conformal-window computation.

Minor objections (5)

[§2, Eq. (2.16) and Eq. (2.17)] The function b-tilde(g(mu)) is defined by the sum in Eq. (2.16) and then claimed to solve Eq. (2.17). The derivation of Eq. (2.17) from Eq. (2.12) is only sketched; a line of algebra would help the reader.
[§3, Eq. (3.5)] The authors correctly note that Eq. (3.5) is scheme dependent, holding 'in the scheme of [10]'. This caveat should be repeated where the result is used in Eq. (3.6), since a reader could otherwise take the closed form for f(g(k)) as scheme independent.
[§2, Eq. (2.28) and §5] The statement that b_IR - b_UV > 0 'contrary to c-theorem intuition' is well taken, but the paper should state explicitly that this is consistent with the absence of a flavor c-theorem rather than evidence against the a-theorem, to avoid confusion between the two central charges.
[Appendix A, Eq. (A.17)] The component anomalies in Eq. (A.17) are given in terms of selfdual and anti-selfdual curvatures; a sentence explaining how the torsionful curvatures of Eq. (A.16) are converted to the torsionless Einstein curvature would make the appendix self-contained.
[References] Reference [9] is listed as 'work in progress' and is cited for the two-loop calculation of the flavor central function that is used as a cross-check in §2. Since the cross-check is part of the paper's support for its general formulas, the relevant result should either be included or the cross-check softened to a statement about the published two-loop results of [6] and [7].

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

In supersymmetric gauge theories that flow between fixed points, the Euler trace anomaly coefficient always decreases from the ultraviolet to the infrared, while the other central charges do not.

The reading

The paper asks whether four-dimensional quantum field theory has a direction built into the renormalization group, the way the two-dimensional central charge does. For $N=1$ supersymmetric gauge theories the authors show the question can be answered exactly, because the trace anomaly, the chiral anomaly of the $R$-current, and the exact Novikov-Shifman-Vainshtein-Zakharov beta function lock together and let the infrared anomalous dimensions be read off without any perturbative expansion. They then compute the flows of the flavor central charge $b$, the stress-tensor central charge $c$, and the Euler anomaly coefficient $a$ for $SU(N_c)$ gauge theory with $N_f$ flavors across the conformal window $3N_c/2 < N_f < 3N_c$. The outcome is a split verdict: $b$ and $c$ fail to be monotonic, but $a_{UV} - a_{IR} > 0$ holds throughout, which is the paper's headline and its main piece of evidence for a four-dimensional analogue of the $c$-theorem.

What carries the argument

The load-bearing object is the anomaly-free combination of the $R$-current and the Konishi current, $S_mu = R_mu + (1/3)(1 - 3N_c/N_f - gamma) K_mu$, whose coefficient is exactly the numerator of the Novikov-Shifman-Vainshtein-Zakharov $\beta$ function. Because $S_mu$ carries no internal anomaly, its external anomaly is one-loop exact and scale independent; 't Hooft anomaly matching then ties the ultraviolet value of a three-point anomaly coefficient to its infrared value, and the vanishing of the $\beta$ function at the infrared fixed point pins the anomalous dimension to $gamma_{IR} = 1 - 3N_c/N_f$. Coupling the conserved current to an external gauge field turns the coefficient of the external trace anomaly into a scale-dependent function that agrees with the central function at fixed points, which is how the flow is extracted without regulating the singular $x to 0$ limit of the correlator; a differential-renormalization identity handles that divergence. A second, independent route treats the external current as a supersymmetric QED photon and reads the same flow off the supersymmetric QED $\beta$ function $beta_e = n(1-gamma)e^3/8pi^2$.

Extended reading notes

Core claim

The central claim is that in $N=1$ supersymmetric $SU(N_c)$ gauge theory with $N_f$ flavors in the conformal window, the Euler trace anomaly coefficient strictly decreases along the flow: $a_{UV} - a_{IR} > 0$ over the whole range $3N_c/2 < N_f < 3N_c$, in both the electric theory and its magnetic dual. The authors obtain this from closed-form infrared values, $c_{IR} = (1/16)(7N_c^2 - 2 - 9N_c^4/N_f^2)$ and $a_{IR} = (3/16)(2N_c^2 - 1 - 3N_c^4/N_f^2)$, compared against the free-field ultraviolet values $c_{UV} = (1/24)(3N_v + N_chi)$ and $a_{UV} = (1/48)(9N_v + N_chi)$. The same computation shows that no such monotonicity survives for the other two charges: the flavor central charge always increases, $b_{IR} - b_{UV} = 6(1 - N_f/3N_c) > 0$, and $c_{IR} - c_{UV}$ changes sign as $N_f$ grows, so there is no supersymmetric $c$-theorem for $c$. The authors are explicit that the flows are not new tests of electric-magnetic duality, since the anomaly-matched current coincides with the $R$-current at the infrared fixed point.

Load-bearing premise

The closed-form answer rests on the infrared fixed point actually existing in the conformal window with anomalous dimension $gamma_{IR} = 1 - 3N_c/N_f$, a value the paper takes from Seiberg duality rather than deriving.

Editorial extensions

If this is right

If the inequality holds beyond supersymmetry, the Euler coefficient becomes a four-dimensional counter of degrees of freedom and the renormalization group acquires a preferred direction.
The sign split among $b$, $c$, and $a$ tells model builders which anomaly coefficients can serve as monotonic counters and which cannot.
Because the infrared values are fixed by anomaly matching, the electric and magnetic descriptions must give the same $a_{IR}$ and $c_{IR}$, a consistency requirement rather than a new duality test.
Integrating out quarks or Higgsing gauge fields gives a more general flow in which $a$ still decreases even though the ultraviolet and infrared field content differ.
The positivity conditions $c_{IR} ge 0$ and $partial a_{IR}/partial N_f ge 0$, imposed on the closed-form answers, restrict where a sensible infrared fixed point can exist at all.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The anomaly-matching strategy should carry over to $N=2$ and $N=4$ superconformal theories, where exactly marginal lines force the anomalous dimensions to vanish; the paper asserts constancy of $b$ there, and one could ask whether $a$ is likewise pinned to its free-field value along such a line.
The method suggests a general tactic for non-supersymmetric theories: whenever a quantity can be tied to a one-loop-exact anomaly of a conserved current, its flow can be computed without solving the strong dynamics, which is precisely what fails for pure Yang-Mills where the infrared is gapped.
If $a$ is the right counter, any proposed four-dimensional analogue of the $c$-theorem should be stated in terms of $a$ rather than $c$; the sign change of $c_{IR} - c_{UV}$ in the electric theory is a concrete obstacle to the $c$ version.
The paper leaves secondary central charges untreated; since those are tied to flavor 't Hooft anomalies through four-point functions, they may offer a finer monotonicity test than $a$ alone.

Original abstract

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,890 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.90 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories.	background 1.00	0.07	0.06	asserted 1.00
s1	We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory.	contribution 0.61	0.96	0.08	asserted 1.00
s2	Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed.	contribution 0.81	0.94	0.11	asserted 1.00
s3	The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$.	result 1.00	0.86	0.56	asserted 1.00
s4	This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow.	interpretation 1.00	0.75	0.41	hedged possibility 0.79
s5	Various other implications are discussed.	contribution 0.66	0.55	0.03	unclear 0.91

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (28)

[8]

D. Anselmi, Central Functions and their Physical Implic ations, preprint CPTH-S493.0197 and hep-th/9702056, January 1997

View on Pith Pith review arXiv 1997
[1]

A.B. Zamolodchikov, “Irreversibility” of the Flux of th e Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730

View on Pith 1986
[2]

N. Seiberg, Electric-Magnetic Duality in Supersymmetr ic Non-Abelian Gauge Theories, Nucl. Phys. B435 (1995) 129

View on Pith 1995
[3]

J.L. Cardy, Is There a c-Theorem in Four Dimensions?, Phys. Lett B215 (1988) 749

View on Pith 1988
[4]

See, for example, Y. Stanev, Bulgarian Journal of Physic s 15 (1988) 93, in d = 4 and A.C. Petkou, Operator Product Expansions and Consistency R elations in the Conformally InvariantO(N ) Vector Model, Ann. Phys. 249 (1996) 180, in 2 <d< 4

View on Pith 1988
[5]

D. Anselmi, M.T. Grisaru and A.A. Johansen, Anomalous Cu rrents, Electric-Magnetic Universality and CFT 4, Nucl. Phys. B491 (1997) 221

View on Pith 1997
[6]

I. Jack, Background Field Calculations in Curved Spacet ime, Nucl. Phys. B253 (1985) 323

View on Pith 1985
[7]

D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A Johansen , Universality of the Operator Product Expansions in SCFT 4, Phys. Lett. B394 (1997) 329

View on Pith 1997
[9]

D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A Johansen , work in progress

View on Pith
[10]

I.I. Kogan, M. Shifman, A. Vainshtein, Matching Condit ions and Duality in N=1 SUSY Gauge Theories in the Conformal Window, Phys. Rev. D53 (1996 ) 4526

View on Pith 1996
[11]

V. Novikov, M.A. Shifman, A.I. Vainshtein, V. Zakharov , Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calc ulus, Nucl. Phys. B229 (1983) 381; 26

View on Pith 1983
[12]

M.A. Shifman and A.I. Vainshtein, Solution of the Anoma ly Puzzle in supersymmetric Gauge Theories and the Wilson Operator Expansion, Nucl. Phy s. B277 (1986) 456

View on Pith 1986
[13]

S.L. Adler, J.C. Collins and A. Duncan, Energy-Momentu m Tensor Trace Anomaly in Spin-1/2 Quantum Electrodynamics, Phys. Rev. D 15 (1977) 17 12

View on Pith 1977
[14]

G. ’t Hooft in Recent Developments in Gauge Theories , Eds. G. ’t Hooft et al . (Plenum Press, New York, 1980); Y. Frishman, A. Schwimmer, T. Banks and S. Yankielowicz, The Axial Anomaly and the Bound-State Spectrum in Conﬁning Theories, Nucl. Phys. B17 7 (1981) 157

View on Pith 1981
[15]

D.Z. Freedman. K. Johnson and J.I. Latorre, Diﬀerential Regularization and Renormal- ization: a New Method of Calculation in Quantum Field Theory , Nucl. Phys. B371 (1992) 353

View on Pith 1992
[16]

M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory , Addison Wesley, Reading, MA (1995)

View on Pith 1995
[17]

A.A. Anselm and A.A. Johansen, Radiative Corrections t o the Axial Anomaly, Zh. Eksp. Teor. Fiz. 96 (1989) 1181

View on Pith 1989
[18]

R.G. Leigh and M.J. Strassler, Exactly Marginal Operat ors and Duality in Four Dimen- sional N=1 Supersymmetric Gauge Theory, Nucl. Phys. B447 (1 995) 95

View on Pith
[19]

S. Christensen and M.J. Duﬀ, Axial and Conformal Anomali es for Arbitrary Spin, Phys. Lett. B76 (1978) 571

View on Pith 1978
[20]

A.D. Dolgov, I.B. Khriplovich, A.I. Vainshtein and V.I . Zakharov, Photonic Chiral Current and its Anomaly in a Gravitational Field, Nucl. Phys. B315 (1 989) 138

View on Pith
[21]

J. Erlich and D.Z. Freedman, Conformal Symmetry and the Chiral Anomaly, hep- th/9611133

View on Pith
[22]

F. Bastianelli, Tests for c-theorems in 4D, Phys. Lett. B 69 (1996) 249

View on Pith 1996
[23]

A. Cappelli, D. Friedan and J.I. Latorre, c-Theorem and Spectral Representation, Nucl. Phys. B352 (1991) 616

View on Pith 1991
[24]

J.I. Latorre and H. Osborn, Positivity and the Energy-M omentum Tensor in Quantum Field Theory, hep-th/9703196

View on Pith Pith review arXiv
[25]

I.N. McArthur, Super- b4 Coeﬃcients in Supergravity, Class. Quantum Grav. 1 (1984) 2 45

View on Pith 1984
[26]

I.L. Buchbinder and S.M. Kuzenko, Matter Superﬁelds in External Supergravity, Nucl. Phys. B274 (1986) 653

View on Pith 1986
[27]

S.J. Gates, M.T. Grisaru, M. Roˇ cek and W. Siegel, Superspace, Addison Wesley, Reading, MA (1983). 27

View on Pith 1983
[28]

I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods in Supersymmetry and Supergravity , Institute of Physics Publishing, Bristol (1995) 28

View on Pith 1995

Forward citations

Showing 60 of 79 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 360 citations worldwide. See all 79 Pith citations

The Exact Superconformal R-Symmetry Maximizes a
hep-th 2003-04 accept novelty 9.0 of 10

The superconformal R-symmetry of any 4d N=1 SCFT is the one that locally maximizes a_trial = (9 Tr R^3 - 3 Tr R)/32, and that maximum is the central charge a.
Carving Out the Space of 4D CFTs
hep-th 2011-09 accept novelty 8.0 of 10

A semidefinite-programming reformulation of the 4D conformal bootstrap yields substantially stronger bounds on operator dimensions, OPE coefficients, central charges and current normalizations, including a bound on di...
On Renormalization Group Flows in Four Dimensions
hep-th 2011-07 conditional novelty 8.0 of 10

The four-dimensional a-theorem is proven: the a-anomaly decreases monotonically along any unitary renormalization group flow, via a positive-definite dispersion relation for dilaton scattering.
The Exact Superconformal R-Symmetry Extremizes Z
hep-th 2010-12 accept novelty 8.0 of 10

The three-sphere partition function of a 3d N=2 theory is extremized at the exact superconformal R-charge, yielding an exact formula for infrared R-charges and chiral operator dimensions.
Conformal collider physics: Energy and charge correlations
hep-th 2008-03 accept novelty 8.0 of 10

Energy correlation functions in conformal field theories are governed at small angles by non-local light-ray operators of definite spin, their one-point antenna patterns are fixed by the anomaly coefficients a and c, ...

Show 55 more citing papers

An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
hep-th 2004-11 accept novelty 8.0 of 10

An infinite family of quiver gauge theories is constructed and shown, via a-maximization, to reproduce exactly the central charges and baryon R-charges computed from the dual Sasaki-Einstein metrics.
Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem
hep-th 1999-04 accept novelty 8.0 of 10

An explicit supersymmetric kink in five-dimensional gauged supergravity realizes a holographic renormalization group flow and yields a monotonic c-function that matches trace anomaly coefficients at both endpoints.
The Holographic Weyl anomaly
hep-th 1998-06 accept novelty 8.0 of 10

The Weyl anomaly of a holographic conformal field theory equals a specific curvature polynomial read off from its dual anti-de Sitter geometry, yielding a new N^3 anomaly for the six-dimensional (0,2) theory.
Anomaly effective actions for 4d $\mathcal{N}=1$ superconformal field theories
hep-th 2026-11 accept novelty 7.0 of 10

The paper constructs the component Wess-Zumino anomaly action for generic 4d N=1 SCFTs to quadratic order in the gravitino, correcting the Q-supersymmetry anomaly for a not equal to c.
DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory
cs.CR 2026-07 conditional novelty 7.0 of 10

Verifier-gated LM repair improves success on broken quiver-gauge-theory claims, but the best exploitation policy reverses between deepseek-chat and qwen-plus.
Non-uniqueness of boundary-value problems in Renormalization Group flows
hep-th 2026-06 unverdicted novelty 7.0 of 10

Boundary-value problems in RG flows are not always unique when the beta-function Jacobian has complex eigenvalues, unlike initial-value problems, with a diagnostic tool and examples in the SM and ASQG.
Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
hep-th 2026-03 unverdicted novelty 7.0 of 10

The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
One Ring to Rule Them All: A Unified Topological Framework for 4D Superconformal Anomalies
hep-th 2025-07 conditional novelty 7.0 of 10

All 4D N=1 superconformal anomalies are shown to fit a single BRST cohomology classification via a constraint ideal, with the a and c anomalies as the two cohomology classes.
N=1 Deformations and RG Flows of N=2 SCFTs
hep-th 2016-07 accept novelty 7.0 of 10

A nilpotent-vev deformation of N=2 SCFTs drives flows that land on N=2 fixed points, giving the first Lagrangian descriptions of the (A1,An) Argyres-Douglas theories.
Deformations of Superconformal Theories
hep-th 2016-02 conditional novelty 7.0 of 10

A symmetry-and-unitarity classification determines which relevant, marginal, and irrelevant supersymmetry-preserving deformations exist for superconformal field theories in three to six dimensions, and which theories ...
On four dimensional N=3 superconformal theories
hep-th 2015-12 accept novelty 7.0 of 10

Any four-dimensional N=3 superconformal theory must have equal conformal anomalies a=c, no exactly marginal deformations, and no global symmetries beyond R-symmetry.
Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
hep-th 2015-06 conditional novelty 7.0 of 10

The a-anomaly of any six-dimensional (1,0) SCFT equals (7/16)(alpha - beta + gamma) + (6/7)delta, a linear combination of its R-symmetry and gravitational 't Hooft anomalies, and this proves the a-theorem for tensor-b...
Interpolating between $a$ and $F$
hep-th 2014-09 accept novelty 7.0 of 10

A dimensionally continued sphere free energy, F-tilde, smoothly interpolates between the a-anomaly in even dimensions and the F value in odd dimensions, and its maximization unifies a-maximization and F-maximization.
Anomaly polynomial of general 6d SCFTs
hep-th 2014-08 accept novelty 7.0 of 10

Anomaly matching on the tensor branch determines the anomaly polynomial of general 6d superconformal theories, including a first derivation for the E-type (2,0) theory.
Cardy Formulae for SUSY Theories in d=4 and d=6
hep-th 2014-07 conditional novelty 7.0 of 10

The high-temperature asymptotics of the 4d N=1 superconformal index is exp(-16 pi^2 (a-c)/(3 beta)), so a-c can be read off from the BPS operator spectrum.
Localization on Hopf surfaces
hep-th 2014-05 conditional novelty 7.0 of 10

The localized partition function on a Hopf surface equals the supersymmetric index times an exact prefactor set by the complex structure moduli and the anomaly coefficients a and c.
New N=1 Dualities
hep-th 2013-03 conditional novelty 7.0 of 10

N=1 SU(N) gauge theory with 2N flavors has a previously unknown dual description in terms of two copies of the T_N theory coupled to 2N^2+2N singlet chiral fields, generalizing the known SU(2) case to all N.
Holographic c-theorems in arbitrary dimensions
hep-th 2010-11 conditional novelty 7.0 of 10

A holographic flow function built from tuned higher-curvature gravity decreases monotonically and equals the A-type trace anomaly coefficient in even dimensions and a universal entanglement-entropy coefficient in all ...
Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
hep-th 2010-11 conditional novelty 7.0 of 10

Trace anomalies are matched across spontaneous breaking of conformal symmetry, and the resulting constraints fix the dilaton effective action, which the authors derive from the Goldstone supermultiplet of broken N=1 s...
Bounds on 4D Conformal and Superconformal Field Theories
hep-th 2010-09 accept novelty 7.0 of 10

Crossing symmetry plus unitarity yields rigorous bounds on central charge, flavor-current strength, and the dimension of the lightest scalar in the chiral-antichiral OPE of 4D N=1 superconformal theories.
Seeing a c-theorem with holography
hep-th 2010-06 conditional novelty 7.0 of 10

In a higher-curvature holographic model with distinct central charges a and c, only a decreases monotonically along renormalization group flows, motivating a conjectured c-theorem in arbitrary dimensions for a univers...
Sicilian gauge theories and N=1 dualities
hep-th 2009-09 conditional novelty 7.0 of 10

Mass-deforming Gaiotto's N=2 triskelion theories produces N=1 superconformal theories that are compactifications of the 6d (2,0) theory with SU(2) Wilson lines, whose gravity duals are the Maldacena-Nunez N=1 solutions.
Central charges of N=2 superconformal field theories in four dimensions
hep-th 2008-04 conditional novelty 7.0 of 10

The central charges a and c of a strongly coupled N=2 SCFT are read off from the R-charge of the topological path-integral measure factor A^chi B^sigma, with no holography required.
Quivers, Tilings, Branes and Rhombi
hep-th 2005-11 conditional novelty 7.0 of 10

A step-by-step algorithm constructs the brane tiling and quiver gauge theory directly from the toric diagram of a toric Calabi-Yau threefold, with R-charges read off as rhombus angles.
Supersymmetric Wilson loops
hep-th 2002-05 conditional novelty 7.0 of 10

Constructs 1/16, 1/8, and 1/4 BPS Wilson loops in N=4 SYM and conjectures that the 1/4 BPS planar loops are not renormalized.
Non-abelian Tensor-multiplet Anomalies
hep-th 1998-08 conditional novelty 7.0 of 10

Assuming M-theory fivebrane anomalies cancel at all charges, the authors derive the exact R-symmetry anomaly polynomial of the A_N (0,2) tensor-multiplet theories and recover the Maldacena-Strominger-Witten black hole...
Decoupling Across Dimensions
hep-th 2026-11 accept novelty 6.0 of 10

A prescription for identifying decoupled sectors in 4d SCFTs from M5-branes using anomaly polynomial comparisons is developed and verified in dual quiver descriptions.
Interpolating between 4d $\mathcal{N}= 1$ SCFT supercurrent multiplet anomalies
hep-th 2026-11 conditional novelty 6.0 of 10

An explicit local counterterm is constructed relating conformal and Ferrara-Zumino supercurrent multiplets of 4d N=1 SCFTs, including new terms independent of the old-minimal auxiliary field.
Entanglement Bounds on Cardy Growth in Higher Dimensions
hep-th 2026-10 conditional novelty 6.0 of 10

Thermal entropy in unitary conformal field theories is conjectured to obey f≤2.9983...F in three dimensions and f≤4π²a in four dimensions, with both bounds saturated by a free real scalar.
Supersymmetric zeta functions and determinants
hep-th 2025-11 conditional novelty 6.0 of 10

Residues and special values of supersymmetric zeta functions (built from single-particle indices) are conjectured to reproduce anomaly coefficients, Casimir energies, and central charges across 2d/4d/6d.
Three-Loop Gauge Beta Functions in Supersymmetric Theories with Exponential Higher Covariant Derivative Regularization
hep-th 2025-09 unverdicted novelty 6.0 of 10

Explicit closed-form evaluation of A(n) and B(m) for exponential regulators R(x)=e^{x^n} and F(x)=e^{x^m} yields fully parameterized three-loop beta functions in general N=1 SUSY gauge theories and demonstrates finite...
A landscape of 4d N=1 SCFTs with a=c
hep-th 2024-12 conditional novelty 6.0 of 10

Starting from an SU(3) gauging of three D2(SU(3)) Argyres-Douglas theories with an adjoint chiral multiplet, the authors map the tree of relevant deformations that preserve a=c and find 21 fixed points, including flow...
Corrections to AdS$_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
hep-th 2022-08 accept novelty 6.0 of 10

The four-derivative corrected on-shell action of the charged rotating AdS5 black hole reproduces the full first line of the second-sheet superconformal index, including the mixed anomaly term, and yields a BPS entropy...
Anomalous Symmetries End at the Boundary
hep-th 2020-12 conditional novelty 6.0 of 10

A symmetry with an 't Hooft anomaly cannot be preserved by any boundary condition of the theory, proven for perturbative and discrete anomalies and conjectured for general gravitational ones.
Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes
hep-th 2020-05 conditional novelty 6.0 of 10

The large-N superconformal index, evaluated on a single conjectured dominant Bethe vacuum, reproduces the Bekenstein-Hawking entropy of BPS Kerr-Newman black holes in AdS5 x S5 and AdS5 x T^{1,1} for arbitrary conserv...
The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index
hep-th 2020-05 conditional novelty 6.0 of 10

For a broad class of 4d N=1 quiver theories, the large-N superconformal index is dominated by saddle points whose effective action is a universal cubic function of the anomaly coefficients.
A 4d N=1 Cardy Formula
hep-th 2019-04 conditional novelty 6.0 of 10

The superconformal index of a 4d N=1 SCFT grows exponentially in the Cardy limit at a rate set by 3c-2a, and its Legendre transform reproduces the Bekenstein-Hawking entropy of AdS5 black holes.
Universal correlation functions in rank 1 SCFTs
hep-th 2018-04 conditional novelty 6.0 of 10

Two-point functions of Coulomb branch chiral primaries in rank-one N=2 SCFTs have a universal large-R-charge expansion log Y_n = J A + B + log Gamma(J + alpha + 1), with all power-law corrections fixed by the a-anomal...
F-theory and AdS_3/CFT_2 (2,0)
hep-th 2017-12 conditional novelty 6.0 of 10

Varying the Type IIB axio-dilaton over the internal space yields new AdS3 solutions dual to 2d (0,2) SCFTs, with holographic and field-theory central charges agreeing to subleading order in N.
Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
hep-th 2017-12 conditional novelty 6.0 of 10

A large higher-spin gap forces the stress tensor to decouple from all other light single-trace operators, with coupling scaling as one over the gap squared, which is the CFT statement that Einstein gravity truncates c...
Lagrangians for generalized Argyres-Douglas theories
hep-th 2017-07 conditional novelty 6.0 of 10

New N=1 quiver Lagrangians are proposed for generalized Argyres-Douglas theories, with the (A_k, A_{kN+N-1}) series as the flagship case, supported by matching central charges and conformal-manifold dimensions.
A Universal Counting of Black Hole Microstates in AdS$_4$
hep-th 2017-07 accept novelty 6.0 of 10

For a large class of 3d N=2 SCFTs with a universal topological twist, the planar-limit twisted index equals (g-1) times the three-sphere free energy, matching the entropy of a universal magnetically charged AdS4 black hole.
Supersymmetric gauge theories with decoupled operators and chiral ring stability
hep-th 2017-06 conditional novelty 6.0 of 10

Adding flipping singlet fields to a four-dimensional N=1 SU(2) gauge theory makes its chiral ring and moduli space match the N=2 A3 Argyres-Douglas theory, and compactifying the completed theory gives a 3d duality wit...
The Cardy limit of the topologically twisted index and black strings in AdS$_5$
hep-th 2016-11 conditional novelty 6.0 of 10

The high-temperature topologically twisted index of a 4d N=1 quiver gauge theory is proportional to the left-moving central charge of the 2d (0,2) SCFT obtained by compactification on S squared.
6d holographic anomaly match as a continuum limit
hep-th 2015-12 accept novelty 6.0 of 10

The a Weyl anomaly of 6d linear quiver theories, computed from the anomaly polynomial, matches the holographic computation from AdS7 crescent-roll solutions in the large-N limit, with the A_{N-1} Cartan matrix acting ...
Two-dimensional SCFTs from D3-branes
hep-th 2015-11 accept novelty 6.0 of 10

Twisted compactification of 4d N=1 Y^{p,q} quivers on a Riemann surface gives 2d N=(0,2) SCFTs whose central charge is (32/3)(g-1) times the 4d a-anomaly, matched by explicit AdS3 solutions of IIB supergravity.
Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
hep-th 2015-05 conditional novelty 6.0 of 10

The a-type Weyl anomaly of every six-dimensional (2,0) superconformal field theory is a_g = (16/7)h^∨_g d_g + r_g, and it decreases along all (2,0)-preserving renormalization group flows.
Cutting through form factors and cross sections of non-protected operators in N=4 SYM
hep-th 2014-10 accept novelty 6.0 of 10

A correction rule lets on-shell unitarity compute Konishi form factors in D=4-2epsilon, yielding two-loop two-point and one-loop three-point results and an infrared-finite decay rate whose logarithm gives the known tw...
Constraints on RG Flow for Four Dimensional Quantum Field Theories
hep-th 2013-12 accept novelty 6.0 of 10

The gradient-flow equations for the a-anomaly hold only for a modified beta function that subtracts a symmetry-rotation term, and the three-loop metric on coupling space is computed and shown to be hermitian in supers...
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
hep-th 2013-09 accept novelty 6.0 of 10

For boundary and defect conformal field theories, the Ryu-Takayanagi holographic entanglement entropy conjecture is proved for hemispherical entangling surfaces, and a probe-brane shortcut computes the leading defect ...
Central charges and RG flow of strongly-coupled N=2 theory
hep-th 2013-01 conditional novelty 6.0 of 10

The authors compute the central charges a, c and k_G for a large class of strongly-coupled N=2 theories, including Argyres-Douglas theories without a 3d mirror, and show their renormalization group flows satisfy the a...
M5-branes from gauge theories on the 5-sphere
hep-th 2012-06 conditional novelty 6.0 of 10

The 5-sphere partition function of 5d maximal SYM, completed non-perturbatively, reproduces the large N supergravity index on AdS_7 x S^4 and exhibits the N^3 scaling of M5-brane degrees of freedom.
Four-Dimensional SCFTs from M5-Branes
hep-th 2012-03 accept novelty 6.0 of 10

An infinite family of 4D N=1 superconformal field theories arises from M5-branes on complex curves with decomposable normal bundles, with central charges computed consistently by anomaly, holography, and quiver methods.
Jet evolution in the N=4 SYM plasma at strong coupling
hep-th 2008-03 conditional novelty 6.0 of 10

A time-dependent AdS/CFT calculation shows an energetic current in a strongly coupled plasma dissipates through successive near-democratic parton branchings, with a lifetime set by the plasma energy density.
A holographic computation of the central charges of d=4, N=2 SCFTs
hep-th 2007-11 conditional novelty 6.0 of 10

Holography yields exact central charges for the N=2 SCFTs from D3-branes at F-theory singularities, matching Argyres-Seiberg for E6 and E7.

See all 79 Pith citations

How later papers used it

144 later papers cite it

Evidence: substantial. 142 of the citing papers share no author with it, and 25 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 181 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

9 later papers by other authors are listed below: 1 built on it, 6 used its method or tool, 1 used its data or values and 1 compared its own results with it.

Builds on it 1 paper

Showed that the same relations between conformal anomalies and 't Hooft anomalies in 4d SCFTs continue to hold for the DCFTs.

Defect $a$-Theorem and $a$-Maximization (2021) · 0.96 · paraphrased: the licence does not allow quoting

Uses its method or tool 6 of 15 papers with this label

Made use of this paper's relationships between R-charges and central charges.

27/32 (2009) · 0.87 · paraphrased: the licence does not allow quoting
Used this paper's well-known formula for the trial a central charge to compute contributions from hypermultiplets, vectormultiplets and other fields.

Lagrangians for generalized Argyres-Douglas theories (2017) · 0.99 · paraphrased: the licence does not allow quoting
Used this paper's trial central charge a, evaluated on the encoded R-symmetry without a-maximization, to require agreement between the two theories.

DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory (2026) · 0.81 · paraphrased: the licence does not allow quoting
Used this paper's relation between the 't Hooft anomalies of the U(1)_R symmetry and the a and c central charges to determine the central charges of the gauge theory.

S-confining gauge theories and supersymmetry enhancements (2023) · 0.95 · paraphrased: the licence does not allow quoting
Computing the $𝒩=1$ $a$ and $c$ central charges [ref] by exploiting the anomalies [ref]-[ref]-[ref] of $D_p[SU(N)]$ and the embedding [ref][We also need that $Tr r=Tr r^3=48(a_𝒩=2-c_𝒩=2)$.] [equation] one also finds that these coincide with those of a chiral in the adjoint of $SU(N)$ and with R-charge $2/(p+1)$.

Deconfinements, Kutasov-Schwimmer dualities and $D_p[SU(N)]$ theories (2024) · Comparison between $𝒞_p[SU(N)]$ and 3d quivers for $D_p[SU(N)]$ · 0.91
Used this paper's standard formulae for the central charges a and c in terms of the fermion R-charges.

Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes (2020) · 0.83 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 3 papers with this label

The anomaly coefficients $a$ and $c$ in these expressions depend on the specific SCFT and are normalized such that for $N_$̧ free chiral and$N_v$free vector multiplets [ref] a=1/48(N_+̧9N_v) , c=1/24(N_+̧3N_v) .$W^2$in [ref] denotes the square of the Weyl tensor, while$E$and$$are respectively the Euler and Pontryagin densities.

Supersymmetric Casimir energy on $\mathcal{N}=1$ conformal supergravity backgrounds (2023) · $=1$ superconformal Ward identities · 0.82

Compares with it 1 of 4 papers with this label

Noted that its own result is indeed the same as the non-perturbative result quoted in this paper when taking into account the explicit form of the parameter.

${\cal N} = 1$ Euler Anomaly Flow from Dilaton Effective Action (2015) · 0.93 · paraphrased: the licence does not allow quoting

How the literature uses it

134 arXiv papers cite this in 170 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 125 sentences without a confident label

Builds on it 1 paper

For the $p=4$ conformal defects preserving the minimal $=1$ SUSY, in Section [ref] we show that the same relations between conformal anomalies and 't Hooft anomalies in 4d SCFTs [ref] continue to hold for the DCFTs.

Defect $a$-Theorem and $a$-Maximization · Introduction and Summary · 0.96

Uses its method or tool 13 papers

In particular, we will make use of the relationships [ref] [equation] where $R$ in this expression is the matrix of R-charges of Weyl fermions in the theory; in a strongly coupled theory $R^3$ and $R$ should be understood as the corresponding anomaly coefficients.

27/32 · Introduction · 0.87
Under the assumption that ([ref]) is the R-symmetry of the IR fixed point, one can immediately evaluate the a and c central charges of our IR fixed point using the well-known formulas [ref] [equation] combined with the relations [ref] [equation] where $a'$ and $c'$ are the central charges of the AD theory (here we are using 't Hooft anomaly matching) given in the previous section.

$\mathcal{N}=2$ Argyres-Douglas theories, $\mathcal{N}=1$ SQCD and Seiberg duality · $SU(2)$ theory with one flavor · 0.98
The $R$-charge family requires the trial central charge $a$ [ref] , evaluated on the encoded $R$-symmetry (no $a$-maximization [ref] is performed), to agree between the two theories.

DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory · : certificates and repair interface · 0.81

Uses its data or values 3 papers

The field theory determination of these anomaly coefficients is [ref] a= 3/32 ( 3 TrR^3 - TrR ) , c= 1/32 ( 9 TrR^3 - 5 TrR ) , where $R$ is the $R$-symmetry charge of the fields and the trace is over all chiral fermion fields.

Holographic Currents and Chern-Simons Terms · Introduction · 0.81
The anomaly coefficients $a$ and $c$ in these expressions depend on the specific SCFT and are normalized such that for $N_$̧ free chiral and$N_v$free vector multiplets [ref] a=1/48(N_+̧9N_v) , c=1/24(N_+̧3N_v) .$W^2$in [ref] denotes the square of the Weyl tensor, while$E$and$$are respectively the Euler and Pontryagin densities.

Supersymmetric Casimir energy on $\mathcal{N}=1$ conformal supergravity backgrounds · $=1$ superconformal Ward identities · 0.82
We will discuss this more in appendix C.] we obtain a regularized result for the vacuum energy that, after recalling the trace anomaly coefficients [ref] a = 3/32 [ 3(r-1)^3 - (r-1) ] , c = 1/32 [ 9(r-1)^3 - 5 (r-1) ] ,

The Casimir Energy in Curved Space and its Supersymmetric Counterpart · Dimensional reduction of a 4d chiral multiplet · 0.92

Compares with it 3 papers

Now, $(_,_) = (0,_*)$ implies $(_,_) = (- _*,0)$ and therefore [equation] We note that [ref] is indeed the same as the non-perturbative result quoted in (Eq.4.18) in [ref] when taking into account the explicit form of $_*$ [ref].

${\cal N} = 1$ Euler Anomaly Flow from Dilaton Effective Action · $Δ|_=1$ from Dilaton effective Action and Konishi anomaly · 0.93
When $c$ is real, it reproduces the results in [ref] (with corrections made in [ref] ).

CP-violating supersymmetry anomaly · CP-violating supersymmetric Weyl anomaly · 0.91
The anomalies of the bosonic currents are in agreement with the results derived in [ref] .

Anomalous Supersymmetry · Introduction · 0.99

Cites it as support 1 paper

Moreover, finite corrections do not occur either [ref] , i.e.

Cutting through form factors and cross sections of non-protected operators in N=4 SYM · BPS cross section up to one-loop order · 1.00

Cites it as background 21 papers

This procedure is the gravitational analog of $a$-maximization [ref] , which in field theory determines the exact superconformal R-symmetry by maximizing the trial $a$-anomaly over all possible R-symmetry mixings.

Holographic origin of $a$-maximization and higher-derivative AdS$_5$/CFT$_4$ · Introduction · 0.82
This shows up in the trace of the energy-momentum tensor $T_ij$ and in the divergence of the R-current $J^i$ as [ref] [equation] where $Ĉ^2$ and $Ê = R̂_ijklR̂^ijkl-4 R̂_ijR̂^ij+R̂^2$ denote the Weyl$^2$ and Euler invariants of the four-dimensional background geometry, respectively, while $F̂_ij$ is the field strength of the background U(1) gauge field that canonically couples to the R-current.

Corrections to AdS$_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity · Dictionary with superconformal anomalies · 0.84
The holographic anomalies for bosonic currents were computed earlier in [ref] (reproducing (and correcting) known field theory results [ref] ), while [ref] obtained the superconformal anomalies in the presence of local supersymmetric scalar couplings.

Supersymmetry anomaly in the superconformal Wess-Zumino model · Introduction and summary of results · 0.87

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [8]

D. Anselmi, Central Functions and their Physical Implic ations, preprint CPTH-S493.0197 and hep-th/9702056, January 1997

View on Pith Pith review arXiv 1997

[2] [1]

A.B. Zamolodchikov, “Irreversibility” of the Flux of th e Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730

View on Pith 1986

[3] [2]

N. Seiberg, Electric-Magnetic Duality in Supersymmetr ic Non-Abelian Gauge Theories, Nucl. Phys. B435 (1995) 129

View on Pith 1995

[4] [3]

J.L. Cardy, Is There a c-Theorem in Four Dimensions?, Phys. Lett B215 (1988) 749

View on Pith 1988

[5] [4]

See, for example, Y. Stanev, Bulgarian Journal of Physic s 15 (1988) 93, in d = 4 and A.C. Petkou, Operator Product Expansions and Consistency R elations in the Conformally InvariantO(N ) Vector Model, Ann. Phys. 249 (1996) 180, in 2 <d< 4

View on Pith 1988

[6] [5]

D. Anselmi, M.T. Grisaru and A.A. Johansen, Anomalous Cu rrents, Electric-Magnetic Universality and CFT 4, Nucl. Phys. B491 (1997) 221

View on Pith 1997

[7] [6]

I. Jack, Background Field Calculations in Curved Spacet ime, Nucl. Phys. B253 (1985) 323

View on Pith 1985

[8] [7]

D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A Johansen , Universality of the Operator Product Expansions in SCFT 4, Phys. Lett. B394 (1997) 329

View on Pith 1997

[9] [9]

D. Anselmi, D.Z. Freedman, M.T. Grisaru and A.A Johansen , work in progress

View on Pith

[10] [10]

I.I. Kogan, M. Shifman, A. Vainshtein, Matching Condit ions and Duality in N=1 SUSY Gauge Theories in the Conformal Window, Phys. Rev. D53 (1996 ) 4526

View on Pith 1996

[11] [11]

V. Novikov, M.A. Shifman, A.I. Vainshtein, V. Zakharov , Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calc ulus, Nucl. Phys. B229 (1983) 381; 26

View on Pith 1983

[12] [12]

M.A. Shifman and A.I. Vainshtein, Solution of the Anoma ly Puzzle in supersymmetric Gauge Theories and the Wilson Operator Expansion, Nucl. Phy s. B277 (1986) 456

View on Pith 1986

[13] [13]

S.L. Adler, J.C. Collins and A. Duncan, Energy-Momentu m Tensor Trace Anomaly in Spin-1/2 Quantum Electrodynamics, Phys. Rev. D 15 (1977) 17 12

View on Pith 1977

[14] [14]

G. ’t Hooft in Recent Developments in Gauge Theories , Eds. G. ’t Hooft et al . (Plenum Press, New York, 1980); Y. Frishman, A. Schwimmer, T. Banks and S. Yankielowicz, The Axial Anomaly and the Bound-State Spectrum in Conﬁning Theories, Nucl. Phys. B17 7 (1981) 157

View on Pith 1981

[15] [15]

D.Z. Freedman. K. Johnson and J.I. Latorre, Diﬀerential Regularization and Renormal- ization: a New Method of Calculation in Quantum Field Theory , Nucl. Phys. B371 (1992) 353

View on Pith 1992

[16] [16]

M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory , Addison Wesley, Reading, MA (1995)

View on Pith 1995

[17] [17]

A.A. Anselm and A.A. Johansen, Radiative Corrections t o the Axial Anomaly, Zh. Eksp. Teor. Fiz. 96 (1989) 1181

View on Pith 1989

[18] [18]

R.G. Leigh and M.J. Strassler, Exactly Marginal Operat ors and Duality in Four Dimen- sional N=1 Supersymmetric Gauge Theory, Nucl. Phys. B447 (1 995) 95

View on Pith

[19] [19]

S. Christensen and M.J. Duﬀ, Axial and Conformal Anomali es for Arbitrary Spin, Phys. Lett. B76 (1978) 571

View on Pith 1978

[20] [20]

A.D. Dolgov, I.B. Khriplovich, A.I. Vainshtein and V.I . Zakharov, Photonic Chiral Current and its Anomaly in a Gravitational Field, Nucl. Phys. B315 (1 989) 138

View on Pith

[21] [21]

J. Erlich and D.Z. Freedman, Conformal Symmetry and the Chiral Anomaly, hep- th/9611133

View on Pith

[22] [22]

F. Bastianelli, Tests for c-theorems in 4D, Phys. Lett. B 69 (1996) 249

View on Pith 1996

[23] [23]

A. Cappelli, D. Friedan and J.I. Latorre, c-Theorem and Spectral Representation, Nucl. Phys. B352 (1991) 616

View on Pith 1991

[24] [24]

J.I. Latorre and H. Osborn, Positivity and the Energy-M omentum Tensor in Quantum Field Theory, hep-th/9703196

View on Pith Pith review arXiv

[25] [25]

I.N. McArthur, Super- b4 Coeﬃcients in Supergravity, Class. Quantum Grav. 1 (1984) 2 45

View on Pith 1984

[26] [26]

I.L. Buchbinder and S.M. Kuzenko, Matter Superﬁelds in External Supergravity, Nucl. Phys. B274 (1986) 653

View on Pith 1986

[27] [27]

S.J. Gates, M.T. Grisaru, M. Roˇ cek and W. Siegel, Superspace, Addison Wesley, Reading, MA (1983). 27

View on Pith 1983

[28] [28]

I.L. Buchbinder and S.M. Kuzenko, Ideas and Methods in Supersymmetry and Supergravity , Institute of Physics Publishing, Bristol (1995) 28

View on Pith 1995