Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization

A. Lerda; A. Testa; L. Griguolo; M. Billo

REVIEW 2 major objections 4 minor 67 references

Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The two-point correlator of chiral/anti-chiral operators in non-conformal N=2 gauge theories, computed by Feynman diagrams in flat space, agrees through two loops with the prediction of supersymmetric localization on a four-sphere.

desk verdict Solid two-loop match between S^4 localization and flat-space perturbation theory in non-conformal N=2 theories; the unproved no-mixing assumption is the one real caveat. read the letter →

arxiv 2505.03940 v2 pith:CGOPEEFC submitted 2025-05-06 hep-th

M. Billo , L. Griguolo , A. Lerda , A. Testa This is my paper · ORCID

classification hep-th

keywords N=2SYMtheorysupersymmetriclocalizationmatrixmodelschiralcorrelatorsnon-conformalgaugetheoriesevanescenttermstwo-pointfunctionsdimensionalregularization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to establish that supersymmetric localization on a four-sphere can be trusted for two-point correlation functions even in N=2 gauge theories whose conformal symmetry is broken by a non-zero $\beta$ function. In the scale regime where the dynamically generated scale $\Lambda$ is much smaller than the inverse sphere radius $1/R$, which is in turn much smaller than the renormalization scale $\mu$, the flat-space Feynman-diagram computation and the $S^4$ localization matrix model give the same renormalized correlator through two loops. The agreement relies on a mechanism the paper makes explicit: evanescent contributions, which vanish in exactly four dimensions, interfere with the ultraviolet poles of the bare coupling and produce finite terms at the next perturbative order. A successful match means localization can serve as a shortcut for protected observables in asymptotically free N=2 theories, where direct diagrammatic calculations become increasingly expensive.

What carries the argument

The load-bearing mechanism is a difference-theory decomposition of the perturbative expansion. Every vector-multiplet loop correction is shared with N=4 SYM, where all correlators vanish in four dimensions, so it can be rewritten as minus the adjoint-hypermultiplet contribution plus an evanescent remainder; only diagrams with matter in representation $\mathcal R$ minus adjoint matter need be evaluated. In a conformal theory the evanescent remainder is harmless, but here it multiplies the $1/\epsilon$ poles of the bare coupling during renormalization and yields finite two-loop corrections, and the paper computes these interference terms explicitly. On the localization side, the matrix model has interaction action $\mathrm{Tr}'\log H(aR)$ with the difference-theory trace $\mathrm{Tr}_{\mathcal R}-\mathrm{Tr}_{\mathrm{adj}}$, whose leading expansion is the quartic vertex $\frac{\zeta(3)}{2}\left(\frac{g^2}{8\pi^2}\right)^2 \mathrm{Tr}'a^4$. The dictionary is completed by identifying the antipodal distance $2R$ on the sphere with the flat-space separation $|x|$ and the matrix-model coupling with the running coupling at that scale.

What would settle it

Compute the flat-space three-loop two-point function of $O_2$ in SU(N) SQCD with $N_f$ fundamental flavours and compare it with the matrix-model prediction in eq. (4.4): a mismatch in the $\zeta(5)$ coefficient would show the localization correspondence does not extend to the conjectured next order. Alternatively, compute the renormalization mixing matrix for the operators $O_2$ and $O_{(2,2)}$; any non-diagonal entry at one or two loops would invalidate the single-$Z_{g_*}$ assumption underlying the two-loop match.

Watch

Extended reading notes

Core claim

The paper's central claim is that in the regime $\Lambda \ll 1/R \ll \mu$, the renormalized two-point correlator of chiral/anti-chiral operators $O_{\vec n}=\prod_i g^{n_i}\,\mathrm{tr}\,\phi^{n_i}$ (multi-trace, gauge-invariant operators built from the complex scalar $\phi$ of the vector multiplet) in $\mathrm{SU}(N)$ N=2 gauge theory with massless hypermultiplets in a generic representation $\mathcal R$ is \begin{equation*} G^*_{\vec n,\vec m}=$g^{{2n}}$$G^{{(0)}}$_{\vec n,\vec m}\left[1+\left(\frac{$g^{2}$}{8\$pi^{2}$}\right)^2 3\zeta(3)\,$C^{{(2)}}$_{\vec n,\vec m}+O($g^{6}$)\right], \end{equation*} with $C^{(2)}_{\vec n,\vec m}=2n(C_{\mathcal R}i_{\mathcal R}-N^2)+\hat G_{\vec n,\vec m}/G^{(0)}_{\vec n,\vec m}$, where $g$ is the running coupling at the separation scale and $C_{\mathcal R}$, $i_{\mathcal R}$ are the Casimir and Dynkin index of the matter representation. The same expression is obtained independently from flat-space diagrams and from the $S^4$ matrix model, and the equality holds only after the evanescent one-loop vector-exchange term is combined with the $1/\epsilon$ poles of the bare coupling. In the matrix model the ubiquitous coefficient $3\zeta(3)$ comes from the symmetry factors of a single quartic vertex rather than from loop integration, which the paper presents as strong evidence that the two descriptions are computing the same object.

Load-bearing premise

Everything rests on the assumption that the composite operators require no independent renormalization or mixing beyond the overall power of the bare coupling in their definition; if chiral/anti-chiral operators mix with same-charge multi-trace operators or acquire their own anomalous dimensions, the single-coupling renormalization used here would not remove all ultraviolet divergences and the match would fail.

Editorial extensions

If this is right

Within the stated scale hierarchy, localization on $S^4$ gives reliable perturbative results for chiral/anti-chiral two-point functions in asymptotically free N=2 theories, not only in superconformal ones.
The evanescent-plus-pole interference identified for Wilson loops in earlier work is shown to operate for local operators as well, suggesting it is the general rule for protected observables in non-conformal N=2 theories.
The matrix model produces explicit higher-order formulas, such as the $\zeta(5)$ terms in eqs. (4.4) and (4.5), that would be very costly to obtain by Feynman diagrams and can be used as concrete predictions.
Outside the perturbative regime, when $\Lambda R \sim 1$, the correspondence is expected to break down through power-like infrared corrections, so the statement of agreement is tied to the hierarchy $\Lambda \ll 1/R \ll \mu$.

Reading between the lines

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

If the two-loop equality is the first sign of a broader equivalence, the matrix model could resum these correlators in the large-N limit of asymptotically free N=2 theories, potentially connecting to a holographic description; the paper names this as work in progress, so this is an inference about where the result leads.
The evanescent-pole interference implies that any dimensional-regularization computation in non-conformal theories must postpone setting $\epsilon=0$ until after coupling renormalization; computations that discard evanescent terms too early will miss finite contributions.
The explicit $\zeta(5)$ predictions for $O_2$ and $O_3$ in SQCD provide a ready-made falsification target: a direct three-loop flat-space calculation for any one value of $N_f$ would test whether the correspondence extends beyond two loops.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Hi, short take on 2505.03940. This is a careful two-loop calculation, and the match with the matrix model is real. It extends the localization/flat-space dictionary from Wilson loops to two-point correlators of chiral/anti-chiral operators in non-conformal N=2 theories, for any matter representation R. The new bits are the evanescent term e_{2,1} for correlators and a diagrammatic matrix-model method that makes the comparison clean. The final formula (2.58)/(3.32) comes out the same from two independent calculations, with the N beta_0 terms cancelling via the color identities (3.31). No fitted constants. That is solid work and I trust the algebra.

The weak point is footnote 10. The authors say the g_B^n factor in the operator definition lets you absorb all UV poles into the coupling renormalization Z_{g*}, so no separate operator renormalization or mixing is needed. In a non-conformal theory the U(1)_R is anomalous, so the usual chiral-ring protection is gone; mixing between same-charge operators like O_4 and O_{2,2} is not obviously absent. The matrix model is built with the same normal-ordering/no-mixing prescription, so the two sides could in principle be wrong in the same way. Having said that, the Feynman-diagram computation is a genuine direct calculation: the one- and two-loop poles are exactly the coupling-renormalization ones, and the finite parts match the matrix model. That is evidence, not bare assumption. But the authors should either prove the absence of mixing or clearly state that they are assuming it; right now the assertion in footnote 10 is weaker than the rest of the paper.

The other thing to know: the regularization embedding from the companion papers [53-55] is imported. It is well-motivated, but anyone citing this result should check that the identification (3.2) between the matrix-model coupling and the running coupling is on solid ground.

Who is this for? The localization/N=2 exact-results crowd. It advances a known program by one more observable class and provides a useful diagrammatic tool. It deserves a serious referee. Send it to review, but ask for a direct treatment of the mixing question.

Referee Report

2 major / 4 minor

Summary. The paper considers SU(N) N=2 gauge theories with massless hypermultiplets in a generic representation R and a non-vanishing beta function. For chiral/anti-chiral operators O_{\vec n} defined with an explicit overall factor g_B^n, the authors compute the two-point function in flat space by Feynman diagrams in dimensional regularization up to order g_B^{2n+4}. They show that the UV poles arrange into a geometric series that is removed by the one-loop coupling renormalization, while the interference of evanescent O(epsilon) terms with the 1/epsilon poles produces finite two-loop corrections. The resulting renormalized correlator is G^* = g^{2n} G^{(0)} [1 + (g^2/8\pi^2)^2 3\zeta(3) C^{(2)} + O(g^6)] with C^{(2)} = 2n(C_R i_R - N^2) + \hat G_{\vec n,\vec m}/G^{(0)}_{\vec n,\vec m}. The same correlator is computed from the localization matrix model on S^4 using a diagrammatic expansion with the quartic interaction (g^2/8\pi^2)^2 \zeta(3)/2 \,\mathrm{Tr}'\,a^4. The two independent computations agree exactly with the same coefficient C^{(2)}. The paper also gives explicit low-dimension examples and three-loop matrix-model predictions in Section 4.

Significance. If the central claim holds, this is an important extension of supersymmetric localization to non-conformal N=2 theories: it shows that, in the regime \Lambda \ll 1/R \ll \mu, S^4 localization reproduces flat-space correlators of protected local operators up to two loops. The agreement is nontrivial because it involves the cancellation of the N\beta_0 terms through the color identities (3.31), and no constant is fitted. The matrix-model diagrammatic method is efficient and yields falsifiable higher-order predictions such as (4.4)-(4.5). The main caveat is that both computations rely on the same assumption about the absence of independent operator renormalization and mixing, which is not established in the manuscript.

major comments (2)

[\S2.5, Eq. (2.58), and footnote 10] The central result (2.58) relies on the assumption that all UV singularities of the composite operators O_{\vec n} can be absorbed into the single coupling renormalization Z_{g*}. Footnote 10 asserts this because O_{\vec n} carries an overall factor g_B^n, but that factor only changes the power of the bare coupling; it does not by itself imply the absence of an operator wave-function renormalization or of mixing with same-charge multi-trace operators. The two-loop calculation in Section 2 verifies the pole structure, but it does not determine the finite part of any operator counterterm, which is precisely what would enter C^{(2)} in (2.59). The matrix-model computation in (3.18)-(3.32) uses the same no-mixing assumption, so the two computations could in principle agree because both omit the same physics. I ask the authors to either prove that the chiral/anti-chiral operators in these non-conformal N=2 theories are protected in this normalization (e.g., from the N=2 chiral-ring structure) and do not mix at this order, or compute the relevant operator renormalization matrix and show that its effect cancels in the two-point functions at order g^{2n+4}.
[\S3.1, Eq. (3.18)] The identification between the normal-ordered matrix-model operators O_{\vec n}(a) in (3.18) and the bare field-theory operators (2.5) is asserted rather than demonstrated. In the field theory O_{\vec n}(x) is a composite operator built from elementary fields at the same point, while in the matrix model normal ordering removes all self-contractions. This equivalence may be standard in conformal cases, but in the non-conformal setting the interplay between normal ordering, the explicit g_B^n factor, and the renormalization prescription should be spelled out. If the normal-ordered basis is not an eigenbasis of the renormalization group, the comparison leading to (3.32) is incomplete. This concern is closely tied to the previous one, and a unified treatment would be welcome.

minor comments (4)

[\S2.5] Footnote 10 is the only place where the operator-renormalization issue is discussed; given that it is the main potential gap, the discussion should be expanded and moved into the main text.
[\S3, Eq. (3.13)] The sentence "all explicit dependence on R has disappeared" is immediately followed by the important qualification that R enters through the running coupling. Please rephrase to avoid the apparent contradiction, for example by saying that the explicit sphere-radius dependence disappears except through the running coupling evaluated at |x|=2R.
[\S3, Eq. (3.2)] The identification of the matrix-model coupling g_* with the MS-bar coupling of Section 2 is essential to the match, but the scheme relation is only quoted from [53,54]. Please state the precise scheme and explain why the log 4 shift is negligible within the stated regime (1.1).
[Appendix B, Eq. (B.5)] The prefactor in G^*_{5,(3,2)} is written as (N^2-2)(N^2-2); this should presumably be (N^2-2)^2. Please check and correct the typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: flat-space Feynman-diagram and localization matrix-model computations are independent derivations that agree on a closed formula, with no fitted parameter or load-bearing self-citation.

full rationale

The central result (2.58)-(2.59) is obtained in Section 2 by an explicit two-loop Feynman-diagram evaluation: the UV singularities are the geometric progression (2.51) removed by the standard Z_g* renormalization (2.52)-(2.53), while the finite two-loop terms come from the difference-theory functions v_{2,2}, v_{4,2}, bv_{4,2} and from the evanescent/UV-pole interference (2.56)-(2.57). The matrix-model result (3.32)-(3.33) is derived independently in Section 3 from the localization action (3.13), normal-ordered operators (3.18), Gaussian contractions, and the color identities (3.31a)-(3.31b) proved in Appendix C. The two computations share only the definition of the operator's color tensor R and the standard one-loop running-coupling identification (3.1)-(3.2); no constant is fitted to force the match, and the 3ζ(3) coefficient arises independently from loop integrals in one derivation and from combinatorial symmetry factors in the other. The paper's heavy self-citation of [52-55] supplies technical two-loop integrals and the previous Wilson-loop analog, but those are published, externally checkable calculations rather than an unverified uniqueness theorem or an ansatz smuggled in by citation. The no-operator-mixing assertion in footnote 10 is an assumption and a possible correctness risk, not a circular step: even if both computations omitted the same operator-mixing physics, that would be a physical gap, not an equivalence of output to input by construction. Accordingly the derivation chain is self-contained and no prediction reduces to its inputs.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim rests on no fitted constants. Inputs are group-theoretic data (N, i_R, C_R, beta_0), the renormalized coupling, and a prior localization embedding regularization. The scale identification M = 2 mu is a scheme choice, not a fit. The main assumptions are the validity of the embedding regularization and the absence of independent operator renormalization.

assumptions (6)

domain assumption One-loop exactness of the beta function in N=2 SYM, beta(g*) = -epsilon g* - beta_0 g*^3/(16 pi^2), with beta_0 = 2(N - i_R).
Used throughout Sections 2 and 3 to relate bare and renormalized couplings and to identify the running coupling; standard for N=2 supersymmetric gauge theories but not derived in this paper.
domain assumption The embedding regularization for i_R < N, adding massive regulator hypermultiplets with i_{R*} = N and decoupling them, yields a well-defined matrix model whose only residual effect is the Gaussian coefficient (3.1).
Inherited from [2,53,54]; load-bearing for the matrix-model side of the matching.
domain assumption Chiral/anti-chiral operators O_n require no independent renormalization beyond the overall g_B^n factor.
Asserted in footnote 10 (page 13); underlies the renormalized correlator (2.58) and the comparison with the matrix model.
domain assumption Two-loop evanescent terms delta'G^(2) contribute only at order g^{2n+6} and can be neglected at the computed order.
Stated in Section 2.4 (page 8); used to truncate the two-loop field-theory calculation.
domain assumption Instanton corrections are exponentially suppressed in the regime Lambda << 1/R << mu and can be neglected.
Stated in Section 3 and footnote 12; defines the regime of validity (3.5).
standard math Standard SU(N) trace and fusion/fission identities used for color factors (Appendix C, Eqs. (C.3)-(C.14)).
Unproved background group theory, well-known in the literature and stated as identities.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization." pith.science (2026). https://pith.science/paper/CGOPEEFC

@misc{pith2026250503940,
  author       = {Pith},
  title        = {Pith review of: Correlators in non-conformal $\mathcalN=2$ gauge theories from localization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CGOPEEFC}},
  note         = {Machine review of arXiv:2505.03940}
}

abstract

We study two-point correlation functions of chiral/anti-chiral operators in SU(N) $\mathcal{N}=2$ gauge theories with massless hyper-multiplets in a representation $\mathcal{R}$ associated with a non-vanishing $\beta$-function. Using supersymmetric localization on the four-sphere $S^4$, these observables can be evaluated by matrix correlators of normal ordered operators. We show that, within a specific regime of validity, standard perturbative calculations based on Feynman diagrams and renormalization procedures in flat space perfectly match the localization predictions up to two loops generalizing and extending previous results. Our analysis highlights that non-trivial interference effects between evanescent terms and the UV poles of the bare coupling are essential for the agreement. On the matrix model side, we employ a direct diagrammatic procedure akin to the Feynman diagram expansion on the field theory description; this simplifies the comparison for generic operators and general matter representation $\mathcal{R}$.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 12 canonical work pages

[1]

Pestun et al.,Localization techniques in quantum field theories, J

V. Pestun et al.,Localization techniques in quantum field theories, J. Phys. A50 (2017), no. 44 440301, [arXiv:1608.02952]

arXiv 2017
[2]

Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun

V. Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71–129, [arXiv:0712.2824]

arXiv 2012
[3]

Baggio, V

M. Baggio, V. Niarchos, and K. Papadodimas,tt∗ equations, localization and exact chiral rings in 4dN =2 SCFTs, JHEP 02 (2015) 122, [arXiv:1409.4212]

arXiv 2015
[4]

Baggio, V

M. Baggio, V. Niarchos, and K. Papadodimas,Exact correlation functions inSU (2)N = 2 superconformal QCD, Phys. Rev. Lett.113 (2014), no. 25 251601, [arXiv:1409.4217]

arXiv 2014
[5]

Gerchkovitz, J

E. Gerchkovitz, J. Gomis, N. Ishtiaque, A. Karasik, Z. Komargodski, and S. S. Pufu, Correlation Functions of Coulomb Branch Operators, JHEP 01 (2017) 103, [arXiv:1602.05971]

arXiv 2017
[6]

Rodriguez-Gomez and J

D. Rodriguez-Gomez and J. G. Russo,Operator mixing in largeN superconformal field theories on S4 and correlators with Wilson loops, JHEP 12 (2016) 120, [arXiv:1607.07878]

arXiv 2016
[7]

Rodriguez-Gomez and J

D. Rodriguez-Gomez and J. G. Russo,Large N Correlation Functions in Superconformal Field Theories, JHEP 06 (2016) 109, [arXiv:1604.07416]

arXiv 2016
[8]

Billò, F

M. Billò, F. Fucito, A. Lerda, J. F. Morales, Y. S. Stanev, and C. Wen,Two-point correlators in N = 2 gauge theories, Nucl. Phys. B926 (2018) 427–466, [arXiv:1705.02909]

arXiv 2018

Show all 67 references

[9]

Billò, F

M. Billò, F. Galvagno, P. Gregori, and A. Lerda,Correlators between Wilson loop and chiral operators inN = 2 conformal gauge theories, JHEP 03 (2018) 193, [arXiv:1802.09813]

2018 arXiv
[10]

Galvagno and M

F. Galvagno and M. Preti,Chiral correlators inN = 2 superconformal quivers, JHEP 05 (2021) 201, [arXiv:2012.15792]

2021 arXiv
[11]

Beccaria, M

M. Beccaria, M. Billò, F. Galvagno, A. Hasan, and A. Lerda,N = 2 Conformal SYM theories at largeN, JHEP 09 (2020) 116, [arXiv:2007.02840]. – 27 –

2020 arXiv
[12]

Fiol and A

B. Fiol and A. R. Fukelman,The planar limit ofN = 2 chiral correlators, JHEP 08 (2021) 032, [arXiv:2106.04553]

2021 arXiv
[13]

Drukker, S

N. Drukker, S. Giombi, R. Ricci, and D. Trancanelli,Supersymmetric Wilson loops on S**3, JHEP 05 (2008) 017, [arXiv:0711.3226]

2008 arXiv
[14]

Bassetto, L

A. Bassetto, L. Griguolo, F. Pucci, and D. Seminara,Supersymmetric Wilson loops at two loops, JHEP 06 (2008) 083, [arXiv:0804.3973]

2008 arXiv
[15]

Pestun,Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops, JHEP 12 (2012) 067, [arXiv:0906.0638]

V. Pestun,Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops, JHEP 12 (2012) 067, [arXiv:0906.0638]

2012 arXiv
[16]

Giombi and V

S. Giombi and V. Pestun,Correlators of local operators and 1/8 BPS Wilson loops on S**2 from 2d YM and matrix models, JHEP 10 (2010) 033, [arXiv:0906.1572]

2010 arXiv
[17]

Andree and D

R. Andree and D. Young,Wilson Loops in N=2 Superconformal Yang-Mills Theory, JHEP 09 (2010) 095, [arXiv:1007.4923]

2010 arXiv
[18]

Billò, F

M. Billò, F. Galvagno, and A. Lerda,BPS wilson loops in generic conformalN = 2 SU(N) SYM theories, JHEP 08 (2019) 108, [arXiv:1906.07085]

2019 arXiv
[19]

orientifold

M. Beccaria, G. V. Dunne, and A. A. Tseytlin,BPS Wilson loop inN = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation, JHEP 07 (2021) 085, [arXiv:2104.12625]

2021 arXiv
[20]

Komatsu and Y

S. Komatsu and Y. Wang,Non-perturbative defect one-point functions in planarN = 4 super-Yang-Mills, Nucl. Phys. B958 (2020) 115120, [arXiv:2004.09514]

2020 arXiv
[21]

Beccaria and A

M. Beccaria and A. Cabo-Bizet,1/N expansion of the D3-D5 defect CFT at strong coupling, JHEP 02 (2023) 208, [arXiv:2212.12415]

2023 arXiv
[22]

Correa, J

D. Correa, J. Henn, J. Maldacena, and A. Sever,An exact formula for the radiation of a moving quark in N=4 super Yang Mills, JHEP 06 (2012) 048, [arXiv:1202.4455]

2012 arXiv
[23]

Bonini, L

M. Bonini, L. Griguolo, M. Preti, and D. Seminara,Bremsstrahlung function, leading Lüscher correction at weak coupling and localization, JHEP 02 (2016) 172, [arXiv:1511.05016]

2016 arXiv
[24]

B. Fiol, E. Gerchkovitz, and Z. Komargodski,Exact Bremsstrahlung Function inN = 2 Superconformal Field Theories, Phys. Rev. Lett.116 (2016), no. 8 081601, [arXiv:1510.01332]

2016 arXiv
[25]

Mitev and E

V. Mitev and E. Pomoni,Exact Bremsstrahlung and Effective Couplings, JHEP 06 (2016) 078, [arXiv:1511.02217]

2016 arXiv
[26]

Bianchi, M

L. Bianchi, M. Billò, F. Galvagno, and A. Lerda,Emitted Radiation and Geometry, JHEP 01 (2020) 075, [arXiv:1910.06332]

2020 arXiv
[27]

D. J. Binder, S. M. Chester, S. S. Pufu and Y. Wang,N = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization, JHEP 12 (2019) 119, [arXiv:1902.06263]

2019 arXiv
[28]

S. M. Chester, M. B. Green, S. S. Pufu, Y. Wang and C. Wen,Modular invariance in superstring theory fromN = 4 super-Yang-Mills, JHEP 11 (2020) 016, [arXiv:1912.13365]

2020 arXiv
[29]

S. M. Chester and S. S. Pufu,Far beyond the planar limit in strongly-coupledN = 4 SYM, JHEP 01 (2021) 103, [arXiv:2003.08412]

2021 arXiv
[31]

H. Paul, E. Perlmutter and H. Raj,Integrated correlators inN = 4 SYM via SL(2,Z) spectral theory, JHEP 01 (2023) 149, [arXiv:2102.09537]

2023 arXiv
[32]

L. F. Alday, S. M. Chester, D. Dorigoni, M. B. Green and C. Wen,Relations between integrated correlators inN = 4 supersymmetric Yang-Mills theory, JHEP 05 (2024) 044, [arXiv:2310.12322]

2024 arXiv
[33]

Brown, F

A. Brown, F. Galvagno and C. Wen,Exact results for giant graviton four-point correlators, JHEP 07 (2024) 049, [arXiv:2403.17263]

2024 arXiv
[34]

Behan, S

C. Behan, S. M. Chester and P. Ferrero,Gluon scattering in AdS at finite string coupling from localization, JHEP 02 (2024) 042, [arXiv:2305.01016]

2024
[35]

Billo, M

M. Billo, M. Frau, A. Lerda and A. Pini,A matrix-model approach to integrated correlators in aN = 2 SYM theory, JHEP 01 (2024) 154, [arXiv:2311.17178]

2024 arXiv
[36]

Pini and P

A. Pini and P. Vallarino,Integrated correlators at strong coupling in an orbifold ofN = 4 SYM, JHEP 06 (2024) 170, [arXiv:2404.03466]

2024 arXiv
[37]

Billo, M

M. Billo, M. Frau, A. Lerda, A. Pini and P. Vallarino,Integrated correlators in aN = 2 SYM theory with fundamental flavors: a matrix-model perspective, JHEP 11 (2024) 172, [arXiv:2407.03509]

2024 arXiv
[38]

Pini,Integrated correlators with a Wilson line in aN = 2 quiver gauge theory at strong coupling, JHEP 01 (2025) 195, [arXiv:2410.17342]

A. Pini,Integrated correlators with a Wilson line in aN = 2 quiver gauge theory at strong coupling, JHEP 01 (2025) 195, [arXiv:2410.17342]

2025 arXiv
[39]

De Lillo, M

L. De Lillo, M. Frau and A. Pini,Integrated line-defect correlators in Sp(N) SCFTs at strong coupling, JHEP 06 (2025) 078, [arXiv:2503.04902]

2025 arXiv
[40]

Beccaria, G

M. Beccaria, G. V. Dunne, and A. A. Tseytlin,Strong coupling expansion of free energy and BPS Wilson loop inN = 2 superconformal models with fundamental hypermultiplets, JHEP 08 (2021) 102, [arXiv:2105.14729]

2021 arXiv
[41]

Beccaria, M

M. Beccaria, M. Billò, M. Frau, A. Lerda, and A. Pini,Exact results in aN = 2 superconformal gauge theory at strong coupling, JHEP 07 (2021) 185, [arXiv:2105.15113]

2021 arXiv
[42]

Billò, M

M. Billò, M. Frau, F. Galvagno, A. Lerda, and A. Pini,Strong-coupling results forN = 2 superconformal quivers and holography, JHEP 10 (2021) 161, [arXiv:2109.00559]

2021 arXiv
[43]

Billò, M

M. Billò, M. Frau, A. Lerda, A. Pini, and P. Vallarino,Structure Constants in N=2 Superconformal Quiver Theories at Strong Coupling and Holography, Phys. Rev. Lett.129 (2022), no. 3 031602, [arXiv:2206.13582]

2022 arXiv
[44]

Billò, M

M. Billò, M. Frau, A. Lerda, A. Pini, and P. Vallarino,Localization vs holography in 4dN = 2 quiver theories, JHEP 10 (2022) 020, [arXiv:2207.08846]

2022 arXiv
[45]

Beccaria, G

M. Beccaria, G. P. Korchemsky, and A. A. Tseytlin,Strong coupling expansion inN superconformal theories and the Bessel kernel, JHEP 09 (2022) 226, [arXiv:2207.11475]

2022 arXiv
[46]

Beccaria, G

M. Beccaria, G. P. Korchemsky, and A. A. Tseytlin,Non-planar corrections in orbifold/orientifoldN = 2 superconformal theories from localization, JHEP 05 (2023) 165, [arXiv:2303.16305]

2023 arXiv
[47]

Billò, M

M. Billò, M. Frau, A. Lerda, A. Pini, and P. Vallarino,Three-point functions in aN = 2 superconformal gauge theory and their strong-coupling limit, JHEP 08 (2022) 199, [arXiv:2202.06990]

2022 arXiv
[48]

Pini and P

A. Pini and P. Vallarino,Defect correlators in aN = 2 SCFT at strong coupling, JHEP 06 (2023) 050, [arXiv:2303.08210]. – 29 –

2023 arXiv
[49]

Pini and P

A. Pini and P. Vallarino,Wilson loop correlators at strong coupling inN = 2 quiver gauge theories, JHEP 11 (2023) 003, [arXiv:2308.03848]

2023 arXiv
[50]

G. P. Korchemsky and A. Testa,Correlation functions in four-dimensional superconformal long circular quivers, arXiv:2501.17223

arXiv
[51]

A. V. Belitsky and G. P. Korchemsky,Circular Wilson loop in N=2* super Yang-Mills theory at two loops and localization, JHEP 04 (2021) 089, [arXiv:2003.10448]

2021 arXiv
[52]

Billò, F

M. Billò, F. Fucito, G. P. Korchemsky, A. Lerda, and J. F. Morales,Two-point correlators in non-conformalN = 2 gauge theories, JHEP 05 (2019) 199, [arXiv:1901.09693]

2019 arXiv
[53]

Billò, L

M. Billò, L. Griguolo, and A. Testa,Remarks on BPS Wilson loops in non-conformalN = 2 gauge theories and localization, JHEP 01 (2024) 160, [arXiv:2311.17692]

2024 arXiv
[54]

Billò, L

M. Billò, L. Griguolo, and A. Testa,1/2 BPS Wilson loops in non-conformal N = 2 gauge theories and localization: a three-loop analysis, arXiv:2410.14847

arXiv
[55]

Billò, L

M. Billò, L. Griguolo, and A. Testa,Supersymmetric localization and non-conformalN = 2 SYM theories in the perturbative regime, arXiv:2407.11222

arXiv
[56]

J. K. Erickson, G. W. Semenoff, and K. Zarembo,Wilson loops in N=4 supersymmetric Yang-Mills theory, Nucl. Phys. B582 (2000) 155–175, [hep-th/0003055]

2000 arXiv
[57]

M. S. Bianchi,Protected and uniformly transcendental, JHEP 09 (2023) 121, [arXiv:2306.06239]

2023 arXiv
[58]

Bason and M

D. Bason and M. Billò,θ-diagram technique forN = 1, d = 4 superfields, Eur. Phys. J. C83 (2023), no. 10 892, [arXiv:2301.11717]

2023 arXiv
[59]

Rey and T

S.-J. Rey and T. Suyama,Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories, JHEP 01 (2011) 136, [arXiv:1001.0016]

2011 arXiv
[60]

Passerini and K

F. Passerini and K. Zarembo,Wilson Loops in N=2 Super-Yang-Mills from Matrix Model, JHEP 09 (2011) 102, [arXiv:1106.5763]. [Erratum: JHEP 10, 065 (2011)]

2011 arXiv
[61]

Bourgine,A Note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory, J

J.-E. Bourgine,A Note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory, J. Phys. A45 (2012) 125403, [arXiv:1111.0384]

2012 arXiv
[62]

J. G. Russo and K. Zarembo,Large N Limit of N=2 SU(N) Gauge Theories from Localization, JHEP 10 (2012) 082, [arXiv:1207.3806]

2012 arXiv
[63]

Baggio, V

M. Baggio, V. Niarchos, K. Papadodimas, and G. Vos,Large-N correlation functions inN = 2 superconformal QCD, JHEP 01 (2017) 101, [arXiv:1610.07612]

2017 arXiv
[64]

Zarembo,Localization and AdS/CFT Correspondence, J

K. Zarembo,Localization and AdS/CFT Correspondence, J. Phys. A50 (2017), no. 44 443011, [arXiv:1608.02963]

2017 arXiv
[65]

Zarembo,Quiver CFT at strong coupling, JHEP 06 (2020) 055, [arXiv:2003.00993]

K. Zarembo,Quiver CFT at strong coupling, JHEP 06 (2020) 055, [arXiv:2003.00993]

2020 arXiv
[66]

B. Fiol, J. Martínez-Montoya, and A. Rios Fukelman,The planar limit ofN = 2 superconformal field theories, JHEP 05 (2020) 136, [arXiv:2003.02879]

2020 arXiv
[67]

Billò, L

M. Billò, L. Griguolo, A. Lerda, and A. Testa,in preparation
[68]

Grozin,Lectures on QED and QCD, in3rd Dubna International Advanced School of Theoretical Physics, 8, 2005

A. Grozin,Lectures on QED and QCD, in3rd Dubna International Advanced School of Theoretical Physics, 8, 2005. hep-ph/0508242. – 30 –

2005 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Pestun et al.,Localization techniques in quantum field theories, J

V. Pestun et al.,Localization techniques in quantum field theories, J. Phys. A50 (2017), no. 44 440301, [arXiv:1608.02952]

arXiv 2017

[2] [2]

Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun

V. Pestun,Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71–129, [arXiv:0712.2824]

arXiv 2012

[3] [3]

Baggio, V

M. Baggio, V. Niarchos, and K. Papadodimas,tt∗ equations, localization and exact chiral rings in 4dN =2 SCFTs, JHEP 02 (2015) 122, [arXiv:1409.4212]

arXiv 2015

[4] [4]

Baggio, V

M. Baggio, V. Niarchos, and K. Papadodimas,Exact correlation functions inSU (2)N = 2 superconformal QCD, Phys. Rev. Lett.113 (2014), no. 25 251601, [arXiv:1409.4217]

arXiv 2014

[5] [5]

Gerchkovitz, J

E. Gerchkovitz, J. Gomis, N. Ishtiaque, A. Karasik, Z. Komargodski, and S. S. Pufu, Correlation Functions of Coulomb Branch Operators, JHEP 01 (2017) 103, [arXiv:1602.05971]

arXiv 2017

[6] [6]

Rodriguez-Gomez and J

D. Rodriguez-Gomez and J. G. Russo,Operator mixing in largeN superconformal field theories on S4 and correlators with Wilson loops, JHEP 12 (2016) 120, [arXiv:1607.07878]

arXiv 2016

[7] [7]

Rodriguez-Gomez and J

D. Rodriguez-Gomez and J. G. Russo,Large N Correlation Functions in Superconformal Field Theories, JHEP 06 (2016) 109, [arXiv:1604.07416]

arXiv 2016

[8] [8]

Billò, F

M. Billò, F. Fucito, A. Lerda, J. F. Morales, Y. S. Stanev, and C. Wen,Two-point correlators in N = 2 gauge theories, Nucl. Phys. B926 (2018) 427–466, [arXiv:1705.02909]

arXiv 2018