Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories

Nathan Seiberg

REVIEW

Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories

Nathan Seiberg

High Energy Physics - Theory · Submitted 8 Feb 1994 · 12 references

Pith's verdict: The Nf = Nc and Nf = Nc + 1 quantum moduli space results hold up; the soft spot is narrower than the reader thinks, and the Nf ≥ Nc + 2 section is honestly flagged as conjecture.

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arXiv IDhep-th/9402044 (version 1)

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CitationNathan Seiberg. "Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories." arXiv:hep-th/9402044 (1994). https://pith.science/paper/NHSOFALO

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Editor's note

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Short version: this is the paper that made the quantum moduli space of N=1 SUSY QCD a real object, and the two central results are solid. For Nf = Nc the classical constraint det M − B B̃ = 0 becomes det M − B B̃ = Λ^{2Nc} (Pf V = Λ^4 for Nc = 2), so the classical singular points are simply not on the quantum space. For Nf = Nc + 1 the space is classically unmodified but the singular points carry new massless composites M, B, B̃ governed by W_eff = (B M B̃ − det M)/Λ^{2Nf−3}. Both are checked by explicit anomaly matching between the microscopic and macroscopic spectra (4.3, 4.5, 4.7, 5.2, 5.3), and the Nf = Nc + 1 superpotential is checked by its equations of motion reproducing the classical constraints (2.9) and by decoupling to fewer flavors. That is real evidence, not decoration, and it is why the paper has lasted. The special points (4.4) and (4.6) with unbroken R symmetry are the nicest part; the anomaly arithmetic there is done carefully and it works. I'd push back on the reader's framing of the soft spot. The exactness of (3.3) is attributed to the explicit instanton calculations of [6][7], and the constraint follows algebraically for every m ≠ 0 — the paper says so itself: 'these relations are true for every m and not only in the limit m → 0.' The m → 0 limit is not where the delicacy lives. The genuinely soft step is the B B̃ term in (4.1): (3.3) gives B = B̃ = 0, so the baryon piece is inferred from uniqueness of the holomorphic modification consistent with the symmetries, backed by the one-instanton origin and by the anomaly matching at B = −B̃ = Λ^{Nf}, M = 0. Standard, and I believe it, but it is an inference rather than a derivation, and it deserves to be named as such. Section 6 is the other honest gap, and the author says so plainly: 'We could not find a simple set of fields which could resolve the singularity' and 'We cannot show that such a scale invariant theory exists for every Nf ≥ Nc + 2.' The Banks–Zaks fixed point argument is a large-Nc expansion, not a proof for all Nf. That is acknowledged, not hidden. Minor: the overlap note with Kaplunovski–Louis [3] is handled cleanly. Who should read it: anyone working on N=1 dynamics, and anyone who wants to see anomaly matching used as a genuine constraint rather than a ritual. Send it to referees.

Referee report

Significance

If correct, this is a foundational result: it identifies the quantum moduli space of SUSY QCD as an exactly computable holomorphic object and shows that the classical singularities are either removed (Nf = Nc) or resolved by new massless composite states (Nf = Nc + 1). The evidence is strong and largely independent: the anomaly coefficients in (4.3), (4.5), (4.7), (5.2) and (5.3) match between the microscopic and macroscopic spectra, and I verified several of them explicitly (for example the SU(6)^3 and U(1)_R^3 conditions in (5.3), and the U(1)_R^3 and U(1)_R conditions in (4.5) and (4.7)). The effective superpotential (5.4) carries the correct R charge, is invariant under all the symmetries, and its equations of motion reproduce the classical constraints (2.9), which is a nontrivial consistency check. The constraint (4.1) reduces correctly under decoupling of heavy flavors, as shown in §4.1. The paper is also explicit about the limits of its own analysis: §6 states that no simple set of fields resolving the origin was found and that the scale-invariant option cannot be established for every Nf ≥ Nc + 2. The results are exact in the holomorphic sector; the Kähler potential is not

Major objections (2)

[§4, Eq. (4.1)] The step from the exact massive-theory expectation values (3.3) to the quantum constraint det M − B B̃ = Λ^{2Nc} is not fully spelled out for the baryonic term. Equation (3.3) gives B = B̃ = 0, so the det M = Λ^{2Nc} piece follows algebraically, but the coefficient and sign of the B B̃ term are asserted rather than derived: the text says only that the modification is 'due to a one instanton effect.' Since this constraint is the central claim of §4, the argument fixing the baryonic term should be stated explicitly, namely that the modification must be a holomorphic function of the fields consistent with SU(Nf) × SU(Nf) × U(1)_B × U(1)_R, must reduce to det M = Λ^{2Nc} when B = B̃ = 0, and must be linear in the one-instanton amplitude. The anomaly matching at the point B = −B̃ = Λ^{Nf}, M = 0 in (4.6)–(4.7) is an independent check and should be advertised as such at this point in the text rather than only later.
[§4.1, Eqs. (4.10)–(4.15)] The function h(t) = ±2√t − 1 in the effective superpotential (4.10) is quoted in Example 2 before any derivation, and the derivation in Example 3 is carried out only for Nc = Nf = 3 and then extended by the sentence 'Generalizing to arbitrary Nf = Nc, it is straightforward to find the equations of motion.' Because (4.10) is what establishes that the singular locus of the M-moduli space hosts massless fields, the general-Nf derivation, or at minimum an explicit statement that the Nc = Nf = 3 case is representative and why, should be supplied. The accompanying remark that 'the two signs correspond to the two values of B and B̃' also needs one sentence of justification, since the sign choice is what selects between the branches of the moduli space.

Minor objections (6)

[§4.1, Eqs. (4.12)–(4.15)] As typeset, Eq. (4.13) is not dimensionally homogeneous: with y dimensionless, b b̃ y^4 is dimensionless while det m Λ^3 y^3 carries mass^6 and (det m Λ^3)^2 carries mass^12. Correspondingly, the small-det m root quoted in (4.14) does not follow from (4.13) by the stated scaling. Please check the normalization of y and the powers of Λ in (4.12)–(4.15).
[§4.1, Example 1] The effective superpotential is written as W_eff = (Nc − n)Λ_L^{(3Nc−n)/(Nc−n)}/det' M, whereas the standard form has det' M raised to the power 1/(Nc − n). Please check this expression.
[§2, Eqs. (2.3)–(2.7)] The parallel treatment of Nc = 2 (the field V) and Nc > 2 (the fields M, B, B̃) doubles many equations and makes the logic harder to follow. A short table summarizing the three regimes Nf = Nc, Nf = Nc + 1, and Nf ≥ Nc + 2, together with the fate of the classical singularities in each, would substantially help the reader.
[Abstract and §6] The sentence 'Alternatively, new massless states appear there' is established for Nf = Nc + 1 (composite mesons and baryons) but is conjectural for Nf ≥ Nc + 2, as §6 acknowledges. Consider making that distinction explicit in the abstract so that the headline claim is not read as covering the entire range of Nf.
[§1 and §6] The paper determines the complex structure of the moduli space but not its Kähler potential. Statements such as the possibility that 'the origin is infinitely far from every point on the moduli space' in §6 are appropriately hedged, but a sentence in §1 delimiting the scope to the holomorphic sector would prevent misreading.
[References] Reference [2] is listed as 'in preparation.' It is cited only for elaboration of related results and not for any result used in this paper, so this does not affect the assessment, but the citation should be updated at proof stage. The overlap with [3] is disclosed in §1 and handled appropriately.

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The paper

The paper claims

Quantum effects replace the singular points of a supersymmetric vacuum space with a smooth one, and in one case with new massless bound states.

The reading

Seiberg asks what happens to the space of ground states of a supersymmetric gauge theory — supersymmetric QCD with $N_c$ colors and $N_f$ quark flavors — once quantum effects are included. Classically that space of vacua has singular points where extra particles become massless and the gauge symmetry is enhanced, and the question is whether those singularities survive quantization. Using exact holomorphic expressions for quark-bilinear expectation values in the massive theory and then taking the quark masses to zero, he argues that for $N_f = N_c$ the classical constraint $M - B = 0$ is replaced by $M - B = 0$, so the classical singular points are simply absent from the quantum moduli space. For $N_f = N_c + 1$ the space is unchanged but its singular points carry new massless composite fields, and for $N_f = N_c + 2$ and beyond he suggests the origin may host massless elementary quarks and gluons at an interacting critical point. The payoff is a set of exact statements about strongly coupled four-dimensional dynamics, cross-checked against 't Hooft anomaly matching between the microscopic and macroscopic spectra.

What carries the argument

The load-bearing device is an exact holomorphic formula for the quark condensates in the massive theory, $M^{i}_{j} = ^{(3N_c - N_f)/N_c}(m)^{1/N_c}(1/m)^{i}_{j}$, fixed by holomorphy and the global symmetry selection rules and asserted to be exact rather than approximate; the quantum moduli space is then read off by taking $m = 0$. The $N_f = N_c$ constraint is implemented in an effective Lagrangian by a Lagrange multiplier field $X$ with $W = X(M - B - ^{2N_f})$, and the $N_f = N_c + 1$ case by $W = (B M B - M)/N_c + 1$. 't Hooft anomaly matching — comparing the anomalies of the high-energy quarks and gluons with those of the low-energy fluctuations of $M$, $B$, $B$ around each candidate vacuum — is the consistency check that makes the identification of the special points credible, and it is applied at each of the three symmetry-breaking patterns.

Extended reading notes

Core claim

The central claim is that the quantum moduli space of massless supersymmetric QCD is not the classical one. For $N_f = N_c$ the classical constraint $M - B = 0$ (or $V = 0$ for $N_c = 2$) is modified by a one-instanton effect to $M - B = 0$, with $V = 0$ when $N_c = 2$; the modification is present for every nonzero mass matrix and survives the massless limit. Consequently the classical singular points — where $B = 0$ and $M$ has at least two vanishing eigenvalues — are not on the quantum moduli space at all, so the singularities are blown up rather than resolved by new light fields. The paper then identifies special points on the deformed space where the global symmetry is enhanced: $M = 0$ breaking $SU(N_f) SU(N_f)$ to the diagonal $SU(N_f)$ with $U(1)_R$ unbroken, and $B = -B = 0$, $M = 0$ leaving the chiral symmetry unbroken and breaking only baryon number. For $N_f = N_c + 1$ the classical constraints do survive the massless limit, so the space is classically unmodified; but the singular points are reinterpreted as locations of new massless composite fields $M$, $B$, $B$ governed by the unique invariant superpotential $W = (B M B - M)/N_c + 1$, whose equations of motion reproduce exactly the classical constraints. For $N_f = N_c + 2$ and larger, no such gauge-invariant description is found, and the paper speculates that the elementary colored fields themselves may be massless at the origin, giving a nontrivial four-dimensional critical point.

Load-bearing premise

The whole $N_f = N_c$ result rests on the assumption that the exact massive-theory condensates, taken to zero quark mass, define the quantum moduli space with no extra light fields or corrections — that is, that the modified constraint holds for every mass matrix and survives the massless limit.

Editorial extensions

If this is right

For $N_f = N_c$, the origin of field space is not a vacuum, so the low-energy effective theory on the quantum moduli space can support solitons that have no counterpart as solitons of the classical moduli space.
The points $M = 0$ and $B = -B = 0$, $M = 0$ give vacua with unbroken $U(1)_R$ and unbroken chiral symmetry respectively, so chiral symmetry breaking in these theories need not follow the naive pairing pattern.
For $N_f = N_c + 1$, the singular points of the classical space are physical: all components of $M$, $B$ and $B$ become massless there, so the full chiral symmetry is restored at the origin.
Adding mass terms, or $bB + bB$, and integrating out heavy fields reproduces the known effective descriptions for fewer flavors, so the $N_f = N_c$ and $N_f = N_c + 1$ pictures nest consistently.
For $N_f = N_c + 2$ and above, if the origin is indeed a scale-invariant interacting fixed point, the theory has a nontrivial infrared limit with anomalous dimensions for the quark bilinears, reachable by tuning the number of flavors.

Reading between the lines

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

If the $N_f = N_c$ constraint holds, then the would-be 'enhanced gauge symmetry' points of the classical space are not physical vacua at all, which removes a whole class of candidate light magnetic degrees of freedom from the low-energy spectrum of these theories.
The same holomorphy-plus-selection-rules move — exact massive condensates, then send masses to zero — looks like a general recipe for computing moduli spaces of other supersymmetric theories with flat directions, and the paper's own later examples of confinement without chiral symmetry breaking fit that template.
The proposal that the $N_f \ge N_c + 2$ origin is a Banks–Zaks-like critical point is the one claim here that is established only in a large-$N_c$ expansion, so a controlled small-$N_c$ check (for instance $N_c = 2$, $N_f = 4$) would be the natural place to look for a counterexample.
The mismatch between the $N_f = N_c$ and $N_f = N_c + 1$ answers suggests the number of flavors acts as a discrete dial separating qualitatively different infrared phases, which is a sharper statement than a gradual crossover and should be visible in the spectrum of the massless theory.

Original abstract

We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless particles. Quantum mechanically these singularities can be smoothed out. Alternatively, new massless states appear there. These may be the elementary massless particles or new massless bound states.

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, 4,074 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless particles. Quantum mechanically these singularities can be smoothed out. Alternatively, new massless states appear there. These may be the elementary massless particles or new massless bound states.

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	We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua.	background 0.63	0.48	0.07	asserted 0.95
s1	Classically, the singular points on the moduli space are associated with extra massless particles.	background 1.00	0.06	0.04	asserted 0.99
s2	Quantum mechanically these singularities can be smoothed out.	background 0.79	0.12	0.07	hedged possibility 0.53
s3	Alternatively, new massless states appear there.	background 0.57	0.16	0.09	asserted 0.52
s4	These may be the elementary massless particles or new massless bound states.	interpretation 0.47	0.12	0.06	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.81.

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
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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 (12)

[6]

I. Aﬄeck, M. Dine, and N. Seiberg, Nucl. Phys. B241 (1984) 493; Nucl. Phys. B256 (1985) 557

View on Pith 1984
[7]

D. Amati, K. Konishi, Y. Meurice, G.C. Rossi and G. Venezi ano, Phys. Rep. 162 (1988) 169 and references therein

View on Pith 1988
[3]

V. Kaplunovski and J. Louis, UTTG-94-1,LMU-TPW-94-1

View on Pith
[1]

N. Seiberg, Phys. Lett. 318B (1993) 469

View on Pith 1993
[2]

K. Intriligator, R. Leigh and N. Seiberg, Rutgers prepri nt, in preparation

View on Pith
[4]

G. Veneziano and S. Yankielowicz, Phys. Lett. 113B (1982 ) 321; T.R. Taylor, G. Veneziano, and S. Yankielowicz, Nucl. Phys. B218 (1983) 493

View on Pith 1983
[5]

A.C. Davis, M. Dine and N. Seiberg, Phys. Lett. 125B (1983 ) 487

View on Pith 1983
[8]

V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zak harov, Nucl. Phys. B223 (1983) 445

View on Pith 1983
[9]

V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zak harov, Nucl. Phys. B260 (1985) 157

View on Pith 1985
[10]

D.R.T. Jones, Nucl. Phys. B75 (1974) 531; R. Barbieri, S . Ferrara, L. Maiani, F. Palumbo and C.Savoy, Phys. Lett. 115B (1982) 212; A. Parkes a nd P. West, Phys. Lett. 138B (1984) 199

View on Pith 1974
[11]

V. Novikov, M. Shifman, A. Vainshtein, M. Voloshin and V . Zakharov, Nucl. Phys. B223 (1983) 394; M.A. Shifman and A.I Vainshtein, Nucl. Phys . B227 (1986) 456

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[12]

T. Banks and A. Zaks, Nucl. Phys. B196 (1982) 189 18

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An axion curvaton with competing Hubble-induced masses generates peaked curvature perturbations that can make primordial black holes all of dark matter and match the NANOGrav signal, linked to a testable dark matter i...
AMSB in Truly Confining Gauge Theories
hep-th 2026-08 conditional novelty 6.0 of 10

Adding small AMSB to t-confining SUSY gauge theories moves the ground state to a superpotential branch and predicts discrete and flavor symmetry breaking such as Z6 to Z2 and Z16 x SU(2) to SO(2).
Krylov Complexity, Confinement and Universality
hep-th 2026-02 conditional novelty 6.0 of 10

Holographic calculations show the proper-momentum proxy for Krylov complexity oscillates in every confining geometry with a smooth infrared cap, with frequency set by the confinement scale.
Loop Corrected Supercharges from Holomorphic Anomalies
hep-th 2025-12 conditional novelty 6.0 of 10

The complete one-loop supercharge for 4d Lagrangian SUSY gauge theories is derived in the holomorphic twist, packaged for N=4 SYM as a compact superfield formula.
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...
Grand-unification Theory Atlas: Standard Model and Beyond
hep-ph 2025-07 conditional novelty 6.0 of 10

A degree-of-freedom count applied to a new atlas of grand-unified gauge theories ranks SU(5) Georgi-Glashow first and SO(10) second for three generations.
Phase Transitions at Unusual Values of $\theta$
hep-th 2025-06 conditional novelty 6.0 of 10

Using Seiberg-Witten theory plus anomaly mediation, the authors find first-order phase transitions in the theta-dependent vacuum energy at theta = pi (N_F=0), 0 and pi (N_F=1), pi/2 and 3pi/2 (N_F=2), and pi/4, 3pi/4,...
Degenerate Domain Walls in Supersymmetric Theories
hep-th 2025-01 conditional novelty 6.0 of 10

In supersymmetric QCD with any number of flavors, the number of degenerate k-domain walls is exactly N!/((N-k)!k!), split into locally distinguishable and topologically distinct classes.
Monopoles, Scattering, and Generalized Symmetries
hep-th 2023-06 conditional novelty 6.0 of 10

Outgoing radiation from fermion-monopole scattering is trailed by a topological surface, often the non-invertible defect D_{2/n}, so it lives in a twisted sector rather than the ordinary Fock space.
On Continuous 2-Category Symmetries and Yang-Mills Theory
hep-th 2022-06 conditional novelty 6.0 of 10

The U(1)^{N-1} semidirect S_N gauge theory carries a continuous non-invertible 1-form symmetry whose largest group-like piece is the Z_N center, and the authors propose it describes the ultraviolet limit of SU(N) Yang-Mills.
Comments on Symmetric Mass Generation in 2d and 4d
hep-th 2021-04 conditional novelty 6.0 of 10

Symmetric mass generation of chiral fermions can be engineered in 2d and 4d by coupling to auxiliary gauge theories that confine without breaking the protected chiral symmetry, with explicit supersymmetric and conject...
$\mathcal{N}{=}1$ supersymmetric indices and the four-dimensional A-model
hep-th 2017-07 conditional novelty 6.0 of 10

The authors derive a sum-over-Bethe-vacua formula for N=1 supersymmetric partition functions on M_{g,p}×S^1, recovering the three-sphere index as a special case and checking it against Seiberg duality.
A "Lagrangian" for a non-Lagrangian theory
hep-th 2015-05 conditional novelty 6.0 of 10

An N=1 gauge theory with a singular superpotential is proposed to flow in the infrared to the N=2 Minahan-Nemeschansky E6 superconformal field theory, reproducing its known anomalies and partition functions.
Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
hep-th 2013-08 conditional novelty 6.0 of 10

Supersymmetric gauge theories are constructed on truncated three- and two-spheres with Dirichlet boundary conditions, and their partition functions and Wilson loops are computed exactly by localization.
3d dualities from 4d dualities for orthogonal groups
hep-th 2013-07 accept novelty 6.0 of 10

Compactifying the 4d SO(N_c) Seiberg duality on a circle yields a 3d duality between SO(N_c) with N_f vectors and SO(N_f - N_c + 2) with N_f vectors plus two singlet fields.
Conformal Dynamics for TeV Physics and Cosmology
hep-ph 2009-11 conditional novelty 6.0 of 10

A conjectured all-orders beta function is used to map the conformal window of SU, Sp and SO gauge theories, extended for the first time to chiral Bars-Yankielowicz and Georgi-Glashow models.
SQCD: A Geometric Apercu
hep-th 2008-03 conditional novelty 6.0 of 10

Using plethystic generating functions and Groebner-basis geometry, the authors compute Hilbert series for N=1 SQCD with arbitrary colours and flavours and argue its vacuum moduli space is an affine Calabi-Yau cone.
Sp(N) higher-derivative F-terms via singular superpotentials
hep-th 2006-03 conditional novelty 6.0 of 10

Sp(N) supersymmetric QCD with enough fundamental flavors has higher-derivative F-terms of a universal form, explicitly verified here for n_f=n_c+1, n_c+2, and n_c+3.
On the Moduli Space of the Cascading SU(M+p)xSU(p) Gauge Theory
hep-th 2005-11 accept novelty 6.0 of 10

The cascading conifold gauge theory's moduli space splits into branches labelled by an R-symmetry integer and a cascade step, each branch a symmetric product of deformed conifolds whose deformation is set by gluino co...
Exact Superpotentials, Quantum Vacua and Duality in Supersymmetric SP(N_c) Gauge Theories
hep-th 1995-05 accept novelty 6.0 of 10

For N=1 supersymmetric SP(N_c) gauge theories with N_f fundamental flavors, the authors derive exact superpotentials, quantum moduli spaces, and a dual magnetic description, with the physics depending on how N_f compa...
Axion Quality Problem: Keep Calm and Baryon
hep-ph 2025-10 conditional novelty 5.0 of 10

The QCD axion can be the Goldstone boson of baryon number in a minimal N_c=N_f supersymmetric QCD sector, with PQ-breaking effects suppressed by dimension N_c+2 operators.
A High Quality Composite Axion
hep-ph 2018-11 conditional novelty 5.0 of 10

A confining supersymmetric SU(N) product gauge theory protects the Peccei-Quinn symmetry to arbitrary order, keeping the strong-CP angle below 10^-11 for an axion decay constant near 10^11 GeV.
Semi-annihilation of Dark Matter
hep-ph 2010-03 accept novelty 5.0 of 10

Semi-annihilation, a reaction that changes dark matter number by one unit, can dominate over ordinary annihilation in setting the relic abundance of multi-component dark matter and produces distinctive monochromatic g...
Lectures on supersymmetric gauge theories and electric-magnetic duality
hep-th 1995-09 accept novelty 4.0 of 10

Holomorphy and electric-magnetic duality organize the infrared phases of four-dimensional supersymmetric gauge theories, with dual magnetic descriptions reproducing the same physics.
Quantum Vortex Strings: A Review
hep-th 2008-09 accept novelty 3.0 of 10

Vortex-string worldsheets provide a quantitative dictionary between two-dimensional sigma models and four-dimensional non-Abelian gauge theories, including exact BPS spectra and supersymmetry-breaking dynamics.
Lectures on Supersymmetry Breaking
hep-ph 2007-02 accept novelty 3.0 of 10

Supersymmetry breaking is organized into four worked mechanisms, with the conclusion that realistic and generic breaking requires living in a long-lived metastable vacuum.
To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories
hep-ph 2025-09 conditional novelty 2.0 of 10

A review showing that if a QCD-like theory with enough massless flavors is fully color-screened in the infrared, then chiral symmetry must be spontaneously broken.

See all 63 Pith citations

How later papers used it

158 later papers cite it

Evidence: substantial. 158 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 21 of the 241 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

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 4 papers with this label

[right] at (-2,-2.6) $= [b_N-2 b_N-2] + [R R]$; at (-0.7,0.4) $l$; at (-1,-0.8) $v_1$; at (0.2,-0.8) $v_2$; at (0.7,-1.6) $…$; at (1.3,-0.8) $v_N-2$; at (1,0.4) $b_N-2$; at (2.7,0.4) $R$; The last $SU(2)$ is once again coupled to $6$ chirals and therefore we can use for the last time the confinement [ref] .

4d N=1 dualities from 5d dualities (2022) · Proof of the 4d dualities · 0.98

How the literature uses it

152 arXiv papers cite this in 235 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 · 172 sentences without a confident label

Uses its method or tool 4 papers

[right] at (-2,-2.6) $= [b_N-2 b_N-2] + [R R]$; at (-0.7,0.4) $l$; at (-1,-0.8) $v_1$; at (0.2,-0.8) $v_2$; at (0.7,-1.6) $…$; at (1.3,-0.8) $v_N-2$; at (1,0.4) $b_N-2$; at (2.7,0.4) $R$; The last $SU(2)$ is once again coupled to $6$ chirals and therefore we can use for the last time the confinement [ref] .

4d N=1 dualities from 5d dualities · Proof of the 4d dualities · 0.98
We will provide such a UV completion in this paper, using a novel application of Seiberg duality [ref] .

125 GeV Higgs from Tree-Level $A$-terms · Introduction · 0.83
where $F_0$ is a holomorphic function of the glueball superfield $S$.[We do not include a detailed expression of the higher-order terms because they contribute only to higher-point gravitational amplitudes, so we do not need them.] Given a tree-level superpotential $W_tree$, the nonperturbative effective potential $W_eff$ can be computed algorithmically, including its gravitational couplings, either via a symmetry and holomorphy analysis [ref] , or through matrix-model methods [ref] .

Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes · Non-perturbative data · 0.98

Uses its data or values 1 paper

The $d_k$ and $d^D_k$ are known instanton coefficients calculated indirectly in [ref] and directly in [ref] .

The Seiberg-Witten Axion · Overview of Seiberg-Witten · 0.85

Compares with it 4 papers

These discussions are completely parallel to the SQCD case [ref] .

N=1 dynamics with T_N theory · Statement of the result · 0.93
In the case of $N=2$ where $(μ_A)_i_A^j_A=Q_i_A i_B i_C Q^j_A i_B i_C$ and $(μ_B)_i_B^j_B=Q_i_A i_B i_C Q^i_A j_B i_C$, one can check that [ref] is just a rewriting of the more familiar deformed moduli constraint $M -B B̃=Λ^4$ of $N_f=N=2$ SUSY QCD [ref] .

Dynamical Supersymmetry Breaking with T_N Theory · The model of supersymmetry breaking · 0.91
[This has to be contrasted with $N=1$ supersymmetric QCD for $N_f=N_c+1$ [ref] , see also [ref] for other supersymmetric gauge theories.

A novel strategy to prove chiral symmetry breaking in QCD-like theories · Introduction · 0.89

Cites it as background 46 papers

This gauge-gauge duality framework was pioneered in a series of ground breaking papers by Seiberg [ref] for supersymmetric gauge theories.

The Standard Model is Natural as Magnetic Gauge Theory · Introduction · 0.86
An essential ingredient of the ISS mechanism is Seiberg duality [ref] : Certain asymptotically free gauge theories, most notably supersymmetric QCD with suitable matter content, are dual to infrared-free gauge theories at energies below their strong-coupling scale $Λ$.

Metastable supersymmetry breaking without scales · Introduction · 0.94
We consider $N=1, SU(N_c)$ SQCD with $N_f$ fundamental flavors $Q, Q̃$ in the free magnetic range [ref]

Dynamically SUSY Breaking SQCD on F-Theory Seven-Branes · Field Theory Requirements · 0.90

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.

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