Abstract
We consider a family of \( \mathcal{N} \) = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of \( \mathcal{N} \) = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the \( \mathcal{N} \) = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from \( \mathcal{N} \) = 4 only at high orders in perturbation theory.
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J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
N. Drukker and D.J. Gross, An exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Supersymmetric Wilson loops on S3 , JHEP 05 (2008) 017 [arXiv:0711.3226] [INSPIRE].
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] [INSPIRE].
S. Giombi and V. Pestun, Correlators of local operators and 1/8 BPS Wilson loops on S2 from 2d YM and matrix models, JHEP 10 (2010) 033 [arXiv:0906.1572] [INSPIRE].
S. Giombi and V. Pestun, The 1/2 BPS ’t Hooft loops in N = 4 SYM as instantons in 2d Yang-Mills, J. Phys. A 46 (2013) 095402 [arXiv:0909.4272] [INSPIRE].
S. Giombi and V. Pestun, Correlators of Wilson Loops and Local Operators from Multi-Matrix Models and Strings in AdS, JHEP 01 (2013) 101 [arXiv:1207.7083] [INSPIRE].
M. Bonini, L. Griguolo and M. Preti, Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory, JHEP 09 (2014) 083 [arXiv:1405.2895] [INSPIRE].
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] [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.-E. Bourgine, A note on the integral equation for the Wilson loop in N = 2 D = 4 superconformal Yang-Mills theory, J. Phys. A 45 (2012) 125403 [arXiv:1111.0384] [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].
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, Operator mixing in large N superconformal field theories on S4 and correlators with Wilson loops, JHEP 12 (2016) 120 [arXiv:1607.07878] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Large N Correlation Functions in Superconformal Field Theories, JHEP 06 (2016) 109 [arXiv:1604.07416] [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].
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. 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].
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. Beccaria, Double scaling limit of N = 2 chiral correlators with Maldacena-Wilson loop, JHEP 02 (2019) 095 [arXiv:1810.10483] [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].
B. Fiol, B. Garolera and G. Torrents, Probing \( \mathcal{N} \) = 2 superconformal field theories with localization, JHEP 01 (2016) 168 [arXiv:1511.00616] [INSPIRE].
A. Bourget, D. Rodriguez-Gomez and J.G. Russo, Universality of Toda equation in \( \mathcal{N} \) = 2 superconformal field theories, JHEP 02 (2019) 011 [arXiv:1810.00840] [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].
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].
S. Kachru and E. Silverstein, 4-D conformal theories and strings on orbifolds, Phys. Rev. Lett. 80 (1998) 4855 [hep-th/9802183] [INSPIRE].
S. Gukov, Comments on N = 2 AdS orbifolds, Phys. Lett. B 439 (1998) 23 [hep-th/9806180] [INSPIRE].
A.E. Lawrence, N. Nekrasov and C. Vafa, On conformal field theories in four-dimensions, Nucl. Phys. B 533 (1998) 199 [hep-th/9803015] [INSPIRE].
A. Gadde, E. Pomoni and L. Rastelli, The Veneziano Limit of N = 2 Superconformal QCD: Towards the String Dual of N = SU(Nc) SYM with Nf = 2Nc, arXiv:0912.4918 [INSPIRE].
A. Gadde, E. Pomoni and L. Rastelli, Spin Chains in \( \mathcal{N} \) = 2 Superconformal Theories: From the ℤ2 Quiver to Superconformal QCD, JHEP 06 (2012) 107 [arXiv:1006.0015] [INSPIRE].
E. Pomoni and C. Sieg, From N = 4 gauge theory to N = 2 conformal QCD: three-loop mixing of scalar composite operators, arXiv:1105.3487 [INSPIRE].
A. Gadde, P. Liendo, L. Rastelli and W. Yan, On the Integrability of Planar N = 2 Superconformal Gauge Theories, JHEP 08 (2013) 015 [arXiv:1211.0271] [INSPIRE].
E. Pomoni, Integrability in N = 2 superconformal gauge theories, Nucl. Phys. B 893 (2015) 21 [arXiv:1310.5709] [INSPIRE].
E. Pomoni, 4D \( \mathcal{N} \) = 2 SCFTs and spin chains, J. Phys. A 53 (2020) 283005 [arXiv:1912.00870] [INSPIRE].
V. Niarchos, C. Papageorgakis and E. Pomoni, Type-B Anomaly Matching and the 6D (2,0) Theory, JHEP 04 (2020) 048 [arXiv:1911.05827] [INSPIRE].
V. Niarchos, C. Papageorgakis, A. Pini and E. Pomoni, (Mis-)Matching Type-B Anomalies on the Higgs Branch, JHEP 01 (2021) 106 [arXiv:2009.08375] [INSPIRE].
V. Mitev and E. Pomoni, Exact effective couplings of four dimensional gauge theories with \( \mathcal{N} \) = 2 supersymmetry, Phys. Rev. D 92 (2015) 125034 [arXiv:1406.3629] [INSPIRE].
V. Mitev and E. Pomoni, Exact Bremsstrahlung and Effective Couplings, JHEP 06 (2016) 078 [arXiv:1511.02217] [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].
K. Zarembo, Quiver CFT at strong coupling, JHEP 06 (2020) 055 [arXiv:2003.00993] [INSPIRE].
H. Ouyang, Wilson loops in circular quiver SCFTs at strong coupling, JHEP 02 (2021) 178 [arXiv:2011.03531] [INSPIRE].
F. Galvagno and M. Preti, Wilson loop correlators in \( \mathcal{N} \) = 2 superconformal quivers, arXiv:2105.00257 [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. Preti, to appear.
B. Fraser, Higher rank Wilson loops in the \( \mathcal{N} \) = 2SU (N) × SU (N) conformal quiver, J. Phys. A 49 (2016) 02LT03 [arXiv:1503.05634] [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].
J. Caetano, O. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP 03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
V. Kazakov, E. Olivucci and M. Preti, Generalized fishnets and exact four-point correlators in chiral CFT4 , JHEP 06 (2019) 078 [arXiv:1901.00011] [INSPIRE].
A. Pittelli and M. Preti, Integrable fishnet from γ-deformed \( \mathcal{N} \) = 2 quivers, Phys. Lett. B 798 (2019) 134971 [arXiv:1906.03680] [INSPIRE].
F. Levkovich-Maslyuk and M. Preti, Exploring the ground state spectrum of γ-deformed N = 4 SYM, arXiv:2003.05811 [INSPIRE].
A. Pittelli and M. Preti, to appear.
F. Galvagno, Wilson loops as defects in N = 2 conformal field theories, arXiv:2005.04019 [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].
M. Preti, STR: a Mathematica package for the method of uniqueness, Int. J. Mod. Phys. C 31 (2020) 2050146 [arXiv:1811.04935] [INSPIRE].
M. Preti, The Game of Triangles, J. Phys. Conf. Ser. 1525 (2020) 012015 [arXiv:1905.07380] [INSPIRE].
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Galvagno, F., Preti, M. Chiral correlators in \( \mathcal{N} \) = 2 superconformal quivers. J. High Energ. Phys. 2021, 201 (2021). https://doi.org/10.1007/JHEP05(2021)201
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DOI: https://doi.org/10.1007/JHEP05(2021)201