Abstract
We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of \( \mathcal{N} \) = 2 SQCD on S4, to all orders in the ’t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ℝ4. Specifically, we compute all the terms with a single value of the ζ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ℝ4.
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References
K. Papadodimas, Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [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, tt* equations, localization and exact chiral rings in 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 02 (2015) 122 [arXiv:1409.4212] [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].
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].
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere Partition Functions and the Zamolodchikov Metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [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].
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].
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. 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].
S. Hellerman, D. Orlando, S. Reffert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge, JHEP 12 (2015) 071 [arXiv:1505.01537] [INSPIRE].
S. Hellerman and S. Maeda, On the Large R-charge Expansion in \( \mathcal{N} \) = 2 Superconformal Field Theories, JHEP 12 (2017) 135 [arXiv:1710.07336] [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].
A. Grassi, Z. Komargodski and L. Tizzano, Extremal correlators and random matrix theory, JHEP 04 (2021) 214 [arXiv:1908.10306] [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, 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].
S. Hellerman and D. Orlando, Large R-charge EFT correlators in N = 2 SQCD, arXiv:2103.05642 [INSPIRE].
F. A. Dolan and H. Osborn, On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys. 307 (2003) 41 [hep-th/0209056] [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].
V. Pestun, M. Zabzine, F. Benini, T. Dimofte, T. T. Dumitrescu, K. Hosomichi, S. Kim, K. Lee, B. Le Floch and M. Marino, et al, Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.0295].
B. Fiol, J. Martínez-Montoya and A. Rios Fukelman, Wilson loops in terms of color invariants, JHEP 05 (2019) 202 [arXiv:1812.06890] [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. 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].
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].
F. Galvagno and M. Preti, Wilson loop correlators in \( \mathcal{N} \) = 2 superconformal quivers, arXiv:2105.00257 [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].
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].
S. R. Das, A. Dhar, A. M. Sengupta and S. R. Wadia, New Critical Behavior in d = 0 Large N Matrix Models, Mod. Phys. Lett. A 5 (1990) 1041 [INSPIRE].
G. P. Korchemsky, Matrix model perturbed by higher order curvature terms, Mod. Phys. Lett. A 7 (1992) 3081 [hep-th/9205014] [INSPIRE].
L. Álvarez-Gaumé, J. L. F. Barbón and C. Crnkovic, A Proposal for strings at D > 1, Nucl. Phys. B 394 (1993) 383 [hep-th/9208026] [INSPIRE].
I. R. Klebanov, Touching random surfaces and Liouville gravity, Phys. Rev. D 51 (1995) 1836 [hep-th/9407167] [INSPIRE].
I. R. Klebanov and A. Hashimoto, Nonperturbative solution of matrix models modified by trace squared terms, Nucl. Phys. B 434 (1995) 264 [hep-th/9409064] [INSPIRE].
A. Grassi and M. Mariño, M-theoretic matrix models, JHEP 02 (2015) 115 [arXiv:1403.4276] [INSPIRE].
W. T. Tutte, A census of slicings, Can. J. Math. 14 (1962) 708.
R. Gopakumar and R. Pius, Correlators in the Simplest Gauge-String Duality, JHEP 03 (2013) 175 [arXiv:1212.1236] [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in \( \mathcal{N} \) = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
J. Gomis and N. Ishtiaque, Kähler potential and ambiguities in 4d \( \mathcal{N} \) = 2 SCFTs, JHEP 04 (2015) 169 [arXiv:1409.5325] [INSPIRE].
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Fiol, B., Fukelman, A.R. The planar limit of \( \mathcal{N} \) = 2 chiral correlators. J. High Energ. Phys. 2021, 32 (2021). https://doi.org/10.1007/JHEP08(2021)032
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DOI: https://doi.org/10.1007/JHEP08(2021)032