Naturalness Versus Supersymmetric Non-renormalization Theorems

N. Seiberg

REVIEW

Naturalness Versus Supersymmetric Non-renormalization Theorems

N. Seiberg

High Energy Physics - Phenomenology · Submitted 30 Sep 1993 · 15 references

Pith's verdict: The paper that turned holomorphy in background couplings into the standard tool for exact N=1 results; the argument is short, checkable, and mostly holds, with §4.4 the one place where a step is asserted rather than derived.

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arXiv IDhep-ph/9309335 (version 1)

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CitationN. Seiberg. "Naturalness Versus Supersymmetric Non-renormalization Theorems." arXiv:hep-ph/9309335 (1993). https://pith.science/paper/H7PSLN4G

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Editor's note

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This is the short paper that made 'treat the superpotential couplings as background chiral superfields' the default move in N=1 exact results. If you work on superpotentials, dynamical SUSY breaking, or anything downstream of Seiberg duality, this is the source of the technique, and it is worth reading in the original because the argument is only a few pages and you can check every step yourself. The abstract's claim [abstract:s3, s4] — that non-perturbative corrections exist but are not generic functions of the fields — is the real content, and it is a genuine reframing of naturalness rather than a slogan about it. The Wess-Zumino rederivation in §4.1 is a clean sanity check on the method, and the agreement of the m >> Lambda and m << Lambda limits in (2.5) and (2.9) with the exact (4.7) is the kind of independent cross-check that makes an analytic argument credible. The paper is also honest about its status: §3 says outright that the arguments are heuristic and assume regularizability preserving all the symmetries. Note that the classifier record's 'limitations: none found' is simply wrong; that caveat is there in the text, and §4.4 adds another one. One credit point: the argument is presented as a generalization of an unpublished note [8], and the paper says so plainly rather than dressing it up. On soft spots, I'd push back on the reader's framing. §4.3 does close: regularity at x -> 0 kills the terms vanishing as x -> infinity, and the independently known lambda' -> 0 limit kills anything growing faster than x. The residual assumption is smoothness of that limit at fixed lambda S, which is constraint 4's own stated caveat, not a hidden gap. The sharper soft spot is §4.4, where f(u,v,w) = 1 + u + alpha v + beta w is asserted with no derivation, and the paper then says in so many words that establishing SUSY breaking requires showing (4.16) is exact, naming the dangerous Lambda^6/Y term it does not rule out. That is a real gap, flagged but not closed, and it is the one place where the conclusion leans on an unproved step. The undetermined alpha and beta are not a problem — they are coefficients of a single allowed term, not fitted parameters — though footnote 3's beta is explicitly a conjecture. For readers: anyone doing exact results or DSB model building. Send it to referees.

Referee report

Significance

If correct, the result is important and broadly useful. It gives a short, physical derivation of a theorem that previously required supergraph technology, and it extends the reach of exact statements into the non-perturbative regime where the standard perturbative argument says nothing. The paper earns credit for several things a referee should name explicitly. The results are parameter-free in the sense that the field dependence of each exact superpotential is fixed by symmetries and limiting behaviour, with only overall constants such as α in Eq. (4.11) left free. The derivations are cross-checked against independent computations in the regimes where those computations are controlled: the m ≫ Λ and m ≪ Λ limits of §2.2 agree in Eqs. (2.5) and (2.9), and §4.2 explains why they must. The application in §4.4 turns a general naturalness-based no-go statement about R symmetries into a concrete, checkable statement about which invariant operator (Λ⁶/Y) must be absent for supersymmetry to break, which is a falsifiable prediction of the framework. The paper is also candid about its own status: §3 states plainly that the arguments are heuristic and assume a regularization preserving all全局

Major objections (2)

[§4.4, Eqs. (4.17)–(4.18)] The passage from the general invariant form (4.17) to the truncated form (4.18), f(u,v,w) = 1 + u + αv + βw, is asserted rather than derived: the text says only that 'the other constraints in section 3 fix the function f(u,v,w) to be of the form (4.18).' This step is load-bearing, because the paper itself states two sentences later that 'to establish that supersymmetry is indeed broken we must show that (4.16) is exact,' and identifies the dangerous invariant Λ⁶/LQd̄ = Λ⁶/Y as the term whose presence would restore supersymmetry. The reader is therefore asked to accept the absence of that term on the strength of an unstated argument. I would ask the author to supply the explicit monomial analysis: write the most general monomial λ_d Y u^a v^b w^c, and state which limit (regularity at u,v,w → 0, the λ′ → 0 limit, the SU(3) and SU(2) anomaly constraints encoded in v and w, or the φ³ growth bound of constraint 3) excludes each unwanted (a,b,c), including the combination that would reproduce Λ⁶/Y. Without that paragraph the supersymmetry-breaking conclusion of §4.4 rests on an assertion, even though the conclusion is very likely correct.
[Abstract versus §3] The abstract states without qualification that the theorem 'applies both perturbatively and non-perturbatively' and that 'certain invariant terms are not generated,' whereas §3 states that 'our arguments are somewhat heuristic' and that the analysis assumes the theory 'can be regularized while preserving all these symmetries' and that there are 'no unexpected anomalies in supersymmetry (or in any other global symmetry).' Since the non-perturbative half of the claim is exactly the part that rests on these assumptions, the abstract should carry the same hedge as §3, for instance by describing the non-perturbative statement as following from symmetry, holomorphy, and weak-coupling constraints under the standard assumptions about regularization. This is a calibration request, not a challenge to the result: the body of the paper is appropriately careful, and the abstract should match it.

Minor objections (7)

[Eqs. (2.2), (2.5), (2.9), (4.6), (4.7)] As typeset, the Affleck-Dine-Seiberg-type expressions place the determinant in the numerator, e.g. Λ^{(3N−Nf)/(N−Nf)} (det Q̄Q)^{1/(N−Nf)} in Eq. (2.2). Dimensional analysis requires the determinant in the denominator: with the determinant in the denominator the exponent sums to (3N−Nf)/(N−Nf) − 2Nf/(N−Nf) = 3, whereas with it in the numerator the sum is (3N+Nf)/(N−Nf), which is not 3. The same applies to Eqs. (2.5), (2.9), (4.6) and (4.7). This is presumably a transcription issue, but it should be corrected throughout so that the formulas are dimensionally consistent as printed.
[§4.3, Eqs. (4.10)–(4.11)] The step from 'f(x) = αx + 1 + smaller terms as x → ∞' plus regularity at x → 0 to the exact result (4.11) is sound, but it relies on two assumptions that are not stated: that f admits an asymptotic expansion in powers of x as x → ∞ at fixed λS, and that the λ′ → 0 limit is smooth in that regime. Constraint 4 in §3 already warns that non-analyticity can arise when fields are integrated out, so a sentence making explicit that here the limit is smooth, and that terms vanishing at infinity are negative powers of x and are therefore excluded by regularity at the origin, would close the argument cleanly.
[§4.4, Eq. (4.18) and footnote 3] The conjecture that the field-independent term β is non-zero, and that it arises from an SU(2) instanton, is confined to footnote 3. Since the main text uses (4.18) as an exact statement, the conjectural status of β should be flagged in the main text as well, so that a reader who skips the footnote does not mistake it for a derived result.
[§2.2, Eq. (2.6)] The derivation of W_eff ∼ mΛ^{2N}/det′Q̄Q for Nf = N is compressed into 'Repeating the instanton analysis of [3] we find that the massless theory has four fermion zero modes' and 'two of the fermion zero modes can be lifted at order m.' One sentence identifying which zero modes are lifted, and by which insertion, would let the reader follow the argument without returning to [3].
[§4.1] The remark that the Wess-Zumino model 'is not expected to exist non-perturbatively because it is not asymptotically free' is stated without support. A reference or a one-line explanation of the obstruction would help, since the surrounding discussion of the holomorphic anomaly depends on the reader accepting that the model is at best a formal perturbative construction.
[§4.4, Eq. (4.12)] The parenthetical remark that 'unlike the fields in the Standard Model this s is an SU(2) singlet' is confusing as written, because s is listed as a color triplet (3,1) and the contrast being drawn is with the Standard Model's SU(2)-doublet Higgs, not with s. Rewording the sentence to say explicitly that s is a color triplet and an SU(2) singlet, and that this is what distinguishes it from the Standard Model field of the same name, would remove the ambiguity.
[§3, constraint 3] The bound that W_eff 'cannot grow faster than φ³ as a field φ → ∞' is described as holding 'in most cases' and is then used quantitatively in §4.3 to restrict the power of S. A forward reference from constraint 3 to its use in §4.3, and a note on the class of theories for which the bound is expected to fail, would make the logic of §4.3 easier to follow.

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The paper

The paper claims

Seiberg argues that the superpotential of a supersymmetric theory is far more rigid than its symmetries alone would allow, and that this rigidity survives non-perturbative corrections.

The reading

Seiberg sets out to show that the superpotential of a supersymmetric field theory — the holomorphic function that fixes the scalar potential and therefore whether supersymmetry can break — is much more constrained than the symmetries of the theory would suggest. The standard perturbative theorem says quantum loops do not renormalize it; the question here is what survives once non-perturbative effects such as instantons are included. His answer is that such effects do generate new terms, but only a small, computable subset of the terms the symmetries allow. The argument is a bookkeeping device raised to a principle: treat every coupling constant as a background chiral field, so that the large symmetry of the coupling-free theory becomes a selection rule, then use holomorphicity and the behaviour of the theory in limiting regimes to pin the answer down. If it holds, exact results in strongly coupled supersymmetric gauge theories become reachable without any approximation scheme, and the naturalness principle fails non-perturbatively — which is exactly what makes dynamical supersymmetry breaking without an R symmetry possible.

What carries the argument

The mechanism is to promote every coupling constant in the bare superpotential to a background chiral superfield with an infinite kinetic term, so that its non-zero value looks like spontaneous breaking of the global symmetry $G$ that exists at zero coupling. Three further constraints do the work: holomorphicity, meaning $W_{eff}$ depends on the couplings but not their conjugates; smoothness as the dynamical scale $ $ goes to zero, which forbids negative powers of $ $ and, in instanton-dominated cases, forbids powers of $ $ smaller than the one-loop beta-function exponent; and the behaviour at weak coupling, where the answer can be read off perturbatively even though $W_{eff}$ may be non-analytic at zero coupling because massless fields are being integrated out. Together these fix the unknown functions in each example to a finite polynomial, and the finiteness is what rules out the extra invariant terms.

Extended reading notes

Core claim

The paper claims a new non-renormalization theorem that applies both perturbatively and non-perturbatively: the effective superpotential $W_{eff}$ of a supersymmetric theory is not a generic function of the fields consistent with the symmetries, because certain invariant terms are simply never generated. The author states this as a violation of naturalness in its full non-perturbative form, and offers it as a replacement for the older supergraph proof of the perturbative theorem. The claim is carried by worked examples rather than by a single formal statement: Wess-Zumino models recover $W_{eff} = m^2 + g^3$ exactly; supersymmetric QCD with one massive quark gives $W_{eff} = (m^3)$ with no higher powers of the mass; a singlet-coupled model gives $W_{eff} = g' S^3 + (gS)^{N_f/N}$, exact in both couplings; and an $SU(3) SU(2)$ model shows that supersymmetry can break dynamically even with no continuous R symmetry, because a term like $^6 LQ d$ that would have restored supersymmetry is not generated. The author is careful to say the arguments are heuristic and assume the theory can be regularized while preserving all the global symmetries.

Load-bearing premise

In the singlet model and in the $SU(3) SU(2)$ model the unknown function of the couplings is asserted to be a finite polynomial — $f(x) = x + 1 +$ smaller terms, and $f(u,v,w) = 1 + u + v + w$ — and nothing in the symmetry, holomorphicity, or asymptotic-freedom constraints proves that the series terminates.

Editorial extensions

If this is right

Exact superpotentials for supersymmetric QCD with masses and singlet couplings follow without any approximation scheme, for example $W_{eff} = \lambda' S^3 + \alpha \Lambda^{(3N-N_f)/N}(\lambda S)^{N_f/N}$ with no higher-order corrections in either coupling.
The naturalness principle fails non-perturbatively: terms consistent with every symmetry of the problem are not generated, so the effective superpotential is not the most general invariant one.
Dynamical supersymmetry breaking is possible in theories with no continuous R symmetry, removing the phenomenological obstruction that had been raised against such models.
The perturbative non-renormalization theorem is rederived without supergraph technology, and the reported holomorphic anomaly in the Wess-Zumino model is identified as an infrared artifact of the 1PI effective action that cannot appear in the Wilsonian one.

Reading between the lines

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

The rigidity is really a statement about which non-perturbative sectors are allowed to contribute: only effects whose power of the dynamical scale matches the one-loop beta function can generate an operator, which suggests a general rule for reading off which instanton sectors can produce which terms.
The paper's sharp distinction between the Wilsonian and 1PI effective actions implies that many reported anomalies in supersymmetric effective actions are bookkeeping of infrared physics rather than genuine failures of the theorem.
Because the device works by treating a coupling as the expectation value of a field, it should transfer directly to settings where a coupling really is a field — the dilaton being the motivating case — giving selection rules for the resulting effective superpotential.
A concrete test of the argument's weakest step is to compute the next orders in the couplings in the singlet model by instanton methods; a non-zero correction there would be a clean counterexample to the claimed exactness.

Original abstract

We give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories. It applies both perturbatively and non-perturbatively. The superpotential is not renormalized in perturbation theory but receives non-perturbative corrections. However, these non-perturbative corrections are {\it not} generic functions of the fields consistent with the symmetries. Certain invariant terms are not generated. This violation of naturalness has applications to dynamical supersymmetry breaking.

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, 4,732 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.18 · 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 give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories. It applies both perturbatively and non-perturbatively. The superpotential is not renormalized in perturbation theory but receives non-perturbative corrections. However, these non-perturbative corrections are {\it not} generic functions of the fields consistent with the symmetries. Certain invariant terms are not generated. This violation of naturalness has applications to dynamical supersymmetry breaking.

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 give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories.	contribution 1.00	0.95	0.24	asserted 1.00
s1	It applies both perturbatively and non-perturbatively.	result 0.69	0.68	0.07	asserted 1.00
s2	The superpotential is not renormalized in perturbation theory but receives non-perturbative corrections.	result 0.80	0.38	0.20	asserted 1.00
s3	However, these non-perturbative corrections are {\it not} generic functions of the fields consistent with the symmetries.	result 0.99	0.79	0.42	asserted 1.00
s4	Certain invariant terms are not generated.	result 0.99	0.76	0.17	asserted 1.00
s5	This violation of naturalness has applications to dynamical supersymmetry breaking.	interpretation 0.99	0.47	0.18	asserted 0.95

What kind of paper the classifier reports this is: theoretical result 1.00 · 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 (15)

[8]

J. Polchinski and N. Seiberg, (1988) unpublished

View on Pith 1988
[1]

G. ’t Hooft, in Recent Developments in Gauge Theories, ed. G. ’t Hooft et.al., (Plenum, New York, 1980)

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[2]

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View on Pith
[3]

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View on Pith 1984
[4]

I. Aﬄeck, M. Dine and N. Seiberg, Phys. Lett. 137B (1984) 1 87; Phys. Rev. Lett. 52 (1984) 493; Phys. Lett. 140B (1984) 59; Nucl. Phys. B256 (198 5) 557

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[5]

G. Veneziano and S. Yankielowicz, Phys. Lett. 113B (1982 ) 321; T.R. Taylor, G. Veneziano, and S. Yankielowicz, Nucl. Phys. B218 (1983) 493 ; V.A. Novikov, M.A. Shifman, A. I. Vainstain and V. I. Zakharov, Nucl. Phys. B223 (1983) 445; M. Peskin, in Problems in Uniﬁcation and Supergravity , ed. G. Farrar and F. Henyey (AIP, New York, 1984)

View on Pith 1983
[6]

G.C. Rossi and G. Veneziano, Phys. Lett. 138B (1984) 195; Y. Meurice and G. Veneziano, Phys. Lett. 141B (1984) 69; D. Amati, G.C. Rossi a nd G. Veneziano, Phys. Lett. 138B (1984) 195; D. Amati, K. Konishi, Y. Meurice , G.C. Rossi and G. Veneziano, Phys. Rep. 162 (1988) 169

View on Pith 1984
[7]

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

View on Pith 1983
[9]

M. Dine and N. Seiberg, Phys. Rev. Lett. 57 (1986) 2625

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[10]

M.A. Shifman and A.I Vainshtein, Nucl. Phys. B277 (1986 ) 456

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[11]

L.J. Dixon, V.S. Kaplunovsky and J. Louis, Nucl. Phys. B 355 (1991) 649

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[12]

M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, HUTP-9 3-A008, hep-th/9302103

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[13]

I. Jack, D.R.T. Jones and P. West, Phys. Lett. 258B (1991 ) 382

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[14]

E. Witten, Nucl. Phys. B188 (1981) 513; Nucl. Phys. B202 (1982) 253

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[15]

A. Nelson and N. Seiberg, UCSD/PTH 93-27, RU-93-42, hep -ph/9309299 13

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The position dependence of the volume-stabilizing nonperturbative superpotential in a warped flux compactification is given by the embedding equation of the wrapped four-cycle, raised to the power 1/N for N coincident...
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.
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...
Primordial Black Holes from Multifield Inflation with Nonminimal Couplings
hep-th 2022-05 conditional novelty 5.0 of 10

A supersymmetric two-field inflation model with nonminimal couplings can generate a spike in the curvature power spectrum large enough to seed primordial black holes, but only after tuning one coupling to about seven digits.
Anomalies, Conformal Manifolds, and Spheres
hep-th 2015-09 accept novelty 5.0 of 10

The trace anomaly of a conformal field theory, viewed as a sigma model on the space of theories, forces that space to be Kähler-Hodge and, the authors argue, to have vanishing Kähler class.
Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
hep-th 2006-03 conditional novelty 4.0 of 10

A doctoral thesis compiling and extending results on non-anticommutative field theory and twistor geometry, establishing Penrose-Ward correspondences and matrix-model equivalences with ADHM and Nahm equations.
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.
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.
A Crash Course in Supersymmetric Field Theory Across Dimensions
hep-th 2026-07 unverdicted novelty 2.0 of 10

Pedagogical crash-course notes on supersymmetric field theory across 2–10 dimensions, organized around recurring structures such as holomorphy, dualities, indices, BPS data, and anomalies.
D-brane Instantons in Type II String Theory
hep-th 2009-02 accept novelty 2.0 of 10

D-brane instantons provide a calculable, zero-mode-driven source of non-perturbative superpotential and other holomorphic couplings in N=1 Type II orientifold compactifications.
In Pursuit of New Paradigms: TASI 2024
hep-ph 2024-12 accept novelty 1.0 of 10

A review of theoretical paradigms, from pNGB Higgs to SUSY, that attempt to explain the smallness of the Higgs mass.
Lectures on Naturalness, String Landscape and Multiverse
hep-th 2020-08 unverdicted novelty 1.0 of 10

Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.
Geometries of Quantum Field Theories
hep-th 2026-09 unverdicted

An English translation of a 2015 Japanese graduate text on the 3d-3d correspondence, presenting localization, quantum dilogarithms, and complex Chern-Simons theory with no new research content.

How later papers used it

83 later papers cite it

Evidence: substantial. 83 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 20 of the 117 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

4 later papers by other authors are listed below: 4 used its method or tool.

Uses its method or tool 4 of 5 papers with this label

Based its argument on holomorphy of the effective superpotential and promoted superpotential coefficients to dynamical chiral fields a la this paper.

Families of Conformal Fixed Points of N=2 Chern-Simons-Matter Theories (2010) · 0.92 · paraphrased: the licence does not allow quoting
Considered a derivation due to this paper that uses the symmetries and holomorphy of SUSY Lagrangians.

TASI 2008 Lectures: Introduction to Supersymmetry and Supersymmetry Breaking (2009) · 0.97 · paraphrased: the licence does not allow quoting
Used a trick from this paper of promoting the λ^I to expectation values of the lowest components of twisted chiral superfields Λ^I.

Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models (2016) · 0.99 · paraphrased: the licence does not allow quoting
Followed a line of reasoning similar to this paper's proof of nonrenormalization theorems for superpotentials in four dimensions.

Perturbative Aspects of Heterotically Deformed CP(N-1) Sigma Model. I (2010) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

77 arXiv papers cite this in 111 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 · 80 sentences without a confident label

Builds on it 1 paper

Similarly to the relativistic case (see [ref] ), one can make a general argument for the non-renormalization of the superpotential in these models, based on its holomorphicity and the symmetries of the theory.

Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories · Non-Renormalization Theorem: A General Proof · 0.80

Uses its method or tool 5 papers

Our general argument will be based on holomorphy of the effective superpotential, and promoting superpotential coefficients to dynamical chiral fields a la Seiberg [ref] .

Families of Conformal Fixed Points of N=2 Chern-Simons-Matter Theories · Introduction · 0.92
This is a standard technique for proving non-renormalization theorems, see e.g. [ref] ; applying it here should lead to the desired [ref], [ref].

Four-dimensional wall-crossing via three-dimensional field theory · A proof of the wall-crossing formula · 0.97
A useful trick [ref] is to promote the $λ^I$ to expectation values of the (lowest components of) twisted chiral superfields $Λ^I$.

Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models · Review of the Bulk Anomaly · 0.99

Cites it as support 2 papers

Due to some powerful non-renormalization theorems [ref] , this formula for the Kähler potential on $ℳ_c$ is not subject to quantum corrections.

Gromov-Witten invariants and localization · Nonlinear sigma models · 0.96
Thus ([ref]) is exact [ref] .

TASI 2008 Lectures: Introduction to Supersymmetry and Supersymmetry Breaking · Superpotential terms · 0.96

Cites it as background 19 papers

There has been much progress in understanding the gauge dynamics of strongly coupled $N=1$ SUSY field theory with $N_c$ color and $N_f≤N_c+1$ flavors [ref] .

Dynamical Supersymmetry Breaking from Meta-stable Vacua in an N=1 Supersymmetric Gauge Theory · Introduction · 1.00
The tractability of Supersymmetric Quantum Field Theories (SQFTs) comes from the existence of $Q$-closed local operators, i.e. those annihilated by the action of some (set of) supercharge(s) [equation] Such operators are useful for understanding SUSY vacua [ref] , deformations and non-renormalization theorems [ref] , and for matching across supersymmetric and holographic dualities [ref] .

Loop Corrected Supercharges from Holomorphic Anomalies · Introduction and Summary · 0.93
In the SUSY theories, there can be no divergence in some quantum corrections, which is known as the non-renormalization theorem [ref] .

Two-loop Anomalous Dimensions for Four-Fermi Operators in Supersymmetric Theories · Introduction · 0.85

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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