Abstract
We study the 3-point functions of single-trace scalar operators in a four-dimensional \( \mathcal{N} \) = 2 SYM theory with gauge group SU(N) and matter in the symmetric plus anti-symmetric representation, which has a vanishing β-function. By mapping this computation to the matrix model arising from localization on a 4-sphere we are able to resum the perturbative expansion in the large-N ’t Hooft limit and derive the behavior of the correlators at strong coupling. Finally, by combining our results on the 3-point functions with those on the 2-point functions that have been recently found, we obtain the normalized 3-point coefficients of this conformal field theory at strong coupling and find that they depend in a simple way on the conformal dimensions of the single-trace operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. Pestun and M. Zabzine, Introduction to localization in quantum field theory, J. Phys. A 50 (2017) 443001 [arXiv:1608.02953] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
P.S. Howe, K.S. Stelle and P.C. West, A Class of Finite Four-Dimensional Supersymmetric Field Theories, Phys. Lett. B 124 (1983) 55 [INSPIRE].
R. Andree and D. Young, Wilson Loops in N = 2 Superconformal Yang-Mills Theory, JHEP 09 (2010) 095 [arXiv:1007.4923] [INSPIRE].
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] [INSPIRE].
F. Passerini and K. Zarembo, Wilson Loops in N = 2 Super-Yang-Mills from Matrix Model, JHEP 09 (2011) 102 [Erratum ibid. 10 (2011) 065] [arXiv:1106.5763] [INSPIRE].
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] [INSPIRE].
J.G. Russo and K. Zarembo, Wilson loops in antisymmetric representations from localization in supersymmetric gauge theories, Rev. Math. Phys. 30 (2018) 1840014 [arXiv:1712.07186] [INSPIRE].
M. Beccaria and A.A. Tseytlin, 1/N expansion of circular Wilson loop in \( \mathcal{N} \) = 2 superconformal SU(N) ×SU (N) quiver, JHEP 04 (2021) 265 [arXiv:2102.07696] [INSPIRE].
M. Beccaria, G.V. Dunne and A.A. Tseytlin, BPS Wilson loop in \( \mathcal{N} \) = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation, JHEP 07 (2021) 085 [arXiv:2104.12625] [INSPIRE].
M. Beccaria, G.V. Dunne and A.A. Tseytlin, Strong coupling expansion of free energy and BPS Wilson loop in \( \mathcal{N} \) = 2 superconformal models with fundamental hypermultiplets, JHEP 08 (2021) 102 [arXiv:2105.14729] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, Exact correlation functions in SU(2)\( \mathcal{N} \) = 2 superconformal QCD, Phys. Rev. Lett. 113 (2014) 251601 [arXiv:1409.4217] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, On exact correlation functions in SU(N) \( \mathcal{N} \) = 2 superconformal QCD, JHEP 11 (2015) 198 [arXiv:1508.03077] [INSPIRE].
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] [INSPIRE].
M. Baggio, V. Niarchos, K. Papadodimas and G. Vos, Large-N correlation functions in \( \mathcal{N} \) = 2 superconformal QCD, JHEP 01 (2017) 101 [arXiv:1610.07612] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Large N Correlation Functions in Superconformal Field Theories, JHEP 06 (2016) 109 [arXiv:1604.07416] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Operator mixing in large N superconformal field theories on S4 and correlators with Wilson loops, JHEP 12 (2016) 120 [arXiv:1607.07878] [INSPIRE].
A. Pini, D. Rodriguez-Gomez and J.G. Russo, Large N correlation functions \( \mathcal{N} \) = 2 superconformal quivers, JHEP 08 (2017) 066 [arXiv:1701.02315] [INSPIRE].
M. Billó, F. Fucito, A. Lerda, J.F. Morales, Y.S. Stanev and C. Wen, Two-point correlators in N = 2 gauge theories, Nucl. Phys. B 926 (2018) 427 [arXiv:1705.02909] [INSPIRE].
A. Bourget, D. Rodriguez-Gomez and J.G. Russo, A limit for large R-charge correlators in \( \mathcal{N} \) = 2 theories, JHEP 05 (2018) 074 [arXiv:1803.00580] [INSPIRE].
M. Beccaria, On the large R-charge \( \mathcal{N} \) = 2 chiral correlators and the Toda equation, JHEP 02 (2019) 009 [arXiv:1809.06280] [INSPIRE].
M. Billò, F. Galvagno and A. Lerda, BPS Wilson loops in generic conformal \( \mathcal{N} \) = 2 SU(N) SYM theories, JHEP 08 (2019) 108 [arXiv:1906.07085] [INSPIRE].
M. Beccaria, F. Galvagno and A. Hasan, \( \mathcal{N} \) = 2 conformal gauge theories at large R-charge: the SU(N) case, JHEP 03 (2020) 160 [arXiv:2001.06645] [INSPIRE].
M. Beccaria, M. Billò, F. Galvagno, A. Hasan and A. Lerda, \( \mathcal{N} \) = 2 Conformal SYM theories at large \( \mathcal{N} \), JHEP 09 (2020) 116 [arXiv:2007.02840] [INSPIRE].
F. Galvagno and M. Preti, Chiral correlators in \( \mathcal{N} \) = 2 superconformal quivers, JHEP 05 (2021) 201 [arXiv:2012.15792] [INSPIRE].
M. Beccaria, M. Billò, M. Frau, A. Lerda and A. Pini, Exact results in a \( \mathcal{N} \) = 2 superconformal gauge theory at strong coupling, JHEP 07 (2021) 185 [arXiv:2105.15113] [INSPIRE].
B. Fiol and A.R. Fukelman, The planar limit of \( \mathcal{N} \) = 2 chiral correlators, JHEP 08 (2021) 032 [arXiv:2106.04553] [INSPIRE].
M. Billó, M. Frau, F. Galvagno, A. Lerda and A. Pini, Strong-coupling results for \( \mathcal{N} \) = 2 superconformal quivers and holography, JHEP 10 (2021) 161 [arXiv:2109.00559] [INSPIRE].
G.W. Semenoff and K. Zarembo, More exact predictions of SUSYM for string theory, Nucl. Phys. B 616 (2001) 34 [hep-th/0106015] [INSPIRE].
M. Billó, F. Galvagno, P. Gregori and A. Lerda, Correlators between Wilson loop and chiral operators in \( \mathcal{N} \) = 2 conformal gauge theories, JHEP 03 (2018) 193 [arXiv:1802.09813] [INSPIRE].
M. Beccaria, Double scaling limit of N = 2 chiral correlators with Maldacena-Wilson loop, JHEP 02 (2019) 095 [arXiv:1810.10483] [INSPIRE].
M. Beccaria and A.A. Tseytlin, On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators, JHEP 01 (2021) 149 [arXiv:2011.02885] [INSPIRE].
F. Galvagno and M. Preti, Wilson loop correlators in \( \mathcal{N} \) = 2 superconformal quivers, JHEP 11 (2021) 023 [arXiv:2105.00257] [INSPIRE].
B. Fiol, J. Martínez-Montoya and A. Rios Fukelman, The planar limit of \( \mathcal{N} \) = 2 superconformal field theories, JHEP 05 (2020) 136 [arXiv:2003.02879] [INSPIRE].
B. Fiol, J. Martfnez-Montoya and A. Rios Fukelman, The planar limit of \( \mathcal{N} \) = 2 superconformal quiver theories, JHEP 08 (2020) 161 [arXiv:2006.06379] [INSPIRE].
B. Fiol and A.R. Fukelman, On the planar free energy of matrix models, JHEP 02 (2022) 078 [arXiv:2111.14783] [INSPIRE].
B. Fiol, E. Gerchkovitz and Z. Komargodski, Exact Bremsstrahlung Function in N = 2 Superconformal Field Theories, Phys. Rev. Lett. 116 (2016) 081601 [arXiv:1510.01332] [INSPIRE].
B. Fiol, B. Garolera and G. Torrents, Probing \( \mathcal{N} \) = 2 superconformal field theories with localization, JHEP 01 (2016) 168 [arXiv:1511.00616] [INSPIRE].
L. Bianchi, M. Lemos and M. Meineri, Line Defects and Radiation in \( \mathcal{N} \) = 2 Conformal Theories, Phys. Rev. Lett. 121 (2018) 141601 [arXiv:1805.04111] [INSPIRE].
L. Bianchi, M. Billò, F. Galvagno and A. Lerda, Emitted Radiation and Geometry, JHEP 01 (2020) 075 [arXiv:1910.06332] [INSPIRE].
F. Galvagno, Emitted radiation in superconformal field theories, Eur. Phys. J. Plus 137 (2022) 143 [arXiv:2112.03841] [INSPIRE].
C. Gomez, A. Mauri and S. Penati, The Bremsstrahlung function of \( \mathcal{N} \) = 2 SCQCD, JHEP 03 (2019) 122 [arXiv:1811.08437] [INSPIRE].
M. Billó, F. Fucito, G.P. Korchemsky, A. Lerda and J.F. Morales, Two-point correlators in non-conformal \( \mathcal{N} \) = 2 gauge theories, JHEP 05 (2019) 199 [arXiv:1901.09693] [INSPIRE].
I.P. Ennes, C. Lozano, S.G. Naculich and H.J. Schnitzer, Elliptic models, type IIB orientifolds and the AdS/CFT correspondence, Nucl. Phys. B 591 (2000) 195 [hep-th/0006140] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
N.I. Usyukina and A.I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett. B 305 (1993) 136 [INSPIRE].
S. Brooks, A. Gelman, G. Jones and X.-L. Meng, Handbook of Markov chain Monte Carlo, CRC press (2011).
J. Park and A.M. Uranga, A Note on superconformal N = 2 theories and orientifolds, Nucl. Phys. B 542 (1999) 139 [hep-th/9808161] [INSPIRE].
S. Gukov, Comments on N = 2 AdS orbifolds, Phys. Lett. B 439 (1998) 23 [hep-th/9806180] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N , Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
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) 031602 [arXiv:2206.13582] [INSPIRE].
M. Billó, M. Frau, A. Lerda, A. Pini and P. Vallarino, Localization vs holography in 4d\( \mathcal{N} \) = 2 quiver theories, arXiv:2207.08846 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2202.06990
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Billò, M., Frau, M., Lerda, A. et al. Three-point functions in a \( \mathcal{N} \) = 2 superconformal gauge theory and their strong-coupling limit. J. High Energ. Phys. 2022, 199 (2022). https://doi.org/10.1007/JHEP08(2022)199
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)199