Abstract
The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/\( {g}_{YM}^2 \), and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order (\( {g}_{YM}^2 \)N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qk f(gYM), where q = e2πiτ and f(gYM) = O(\( {g}_{YM}^{-2w} \)) when \( {g}_{YM}^2 \) ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form \( {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) \), where \( \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) \) when \( {g}_{YM}^2 \) ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Dorigoni, M.B. Green and C. Wen, Novel Representation of an Integrated Correlator in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 126 (2021) 161601 [arXiv:2102.08305] [INSPIRE].
D. Dorigoni, M.B. Green and C. Wen, Exact properties of an integrated correlator in \( \mathcal{N} \) = 4 SU(N) SYM, JHEP 05 (2021) 089 [arXiv:2102.09537] [INSPIRE].
D.J. Binder, S.M. Chester, S.S. Pufu and Y. Wang, \( \mathcal{N} \) = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization, JHEP 12 (2019) 119 [arXiv:1902.06263] [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].
S.M. Chester, Genus-2 holographic correlator on AdS5 × S5 from localization, JHEP 04 (2020) 193 [arXiv:1908.05247] [INSPIRE].
S.M. Chester, M.B. Green, S.S. Pufu, Y. Wang and C. Wen, Modular invariance in superstring theory from \( \mathcal{N} \) = 4 super-Yang-Mills, JHEP 11 (2020) 016 [arXiv:1912.13365] [INSPIRE].
C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
E. Witten and D.I. Olive, Supersymmetry Algebras That Include Topological Charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].
H. Osborn, Topological Charges for N = 4 Supersymmetric Gauge Theories and Monopoles of Spin 1, Phys. Lett. B 83 (1979) 321 [INSPIRE].
S.M. Chester and S.S. Pufu, Far beyond the planar limit in strongly-coupled \( \mathcal{N} \) = 4 SYM, JHEP 01 (2021) 103 [arXiv:2003.08412] [INSPIRE].
S.M. Chester, M.B. Green, S.S. Pufu, Y. Wang and C. Wen, New modular invariants in \( \mathcal{N} \) = 4 Super-Yang-Mills theory, JHEP 04 (2021) 212 [arXiv:2008.02713] [INSPIRE].
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].
M.B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061] [INSPIRE].
M.B. Green, H.-h. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].
M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].
K.A. Intriligator, Bonus symmetries of N = 4 superYang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].
M.B. Green, Interconnections between type-II superstrings, M-theory and N = 4 supersymmetric Yang-Mills, Lect. Notes Phys. 525 (1999) 22 [hep-th/9903124] [INSPIRE].
B. Eden, P.S. Howe and P.C. West, Nilpotent invariants in N = 4 SYM, Phys. Lett. B 463 (1999) 19 [hep-th/9905085] [INSPIRE].
M.B. Green and C. Wen, Maximal U(1)Y-violating n-point correlators in \( \mathcal{N} \) = 4 super-Yang-Mills theory, JHEP 02 (2021) 042 [arXiv:2009.01211] [INSPIRE].
M.B. Green and C. Wen, Modular Forms and SL(2, ℤ)-covariance of type IIB superstring theory, JHEP 06 (2019) 087 [arXiv:1904.13394] [INSPIRE].
P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Explicit construction of nilpotent covariants in N = 4 SYM, Nucl. Phys. B 571 (2000) 71 [hep-th/9910011] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Towards the Virasoro-Shapiro amplitude in AdS5 × S5, JHEP 04 (2021) 237 [arXiv:2012.12091] [INSPIRE].
A. Basu, M.B. Green and S. Sethi, A Curious truncation of N = 4 Yang-Mills, Phys. Rev. Lett. 93 (2004) 261601 [hep-th/0406267] [INSPIRE].
A. Basu, M.B. Green and S. Sethi, Some systematics of the coupling constant dependence of N = 4 Yang-Mills, JHEP 09 (2004) 045 [hep-th/0406231] [INSPIRE].
P. Di Vecchia, R. Marotta, M. Mojaza and J. Nohle, New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order, Phys. Rev. D 93 (2016) 085015 [arXiv:1512.03316] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].
M.B. Green, M. Gutperle and H.-h. Kwon, Sixteen fermion and related terms in M-theory on T2, Phys. Lett. B 421 (1998) 149 [hep-th/9710151] [INSPIRE].
N. Dorey, T.J. Hollowood, V.V. Khoze, M.P. Mattis and S. Vandoren, Multi-instanton calculus and the AdS/CFT correspondence in N = 4 superconformal field theory, Nucl. Phys. B 552 (1999) 88 [hep-th/9901128] [INSPIRE].
M.B. Green and S. Kovacs, Instanton induced Yang-Mills correlation functions at large N and their AdS5 × S5 duals, JHEP 04 (2003) 058 [hep-th/0212332] [INSPIRE].
G. Arutyunov, D. Dorigoni and S. Savin, Resurgence of the dressing phase for AdS5 × S5, JHEP 01 (2017) 055 [arXiv:1608.03797] [INSPIRE].
B. Basso, G.P. Korchemsky and J. Kotanski, Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. Lett. 100 (2008) 091601 [arXiv:0708.3933] [INSPIRE].
I. Aniceto, The Resurgence of the Cusp Anomalous Dimension, J. Phys. A 49 (2016) 065403 [arXiv:1506.03388] [INSPIRE].
D. Dorigoni and Y. Hatsuda, Resurgence of the Cusp Anomalous Dimension, JHEP 09 (2015) 138 [arXiv:1506.03763] [INSPIRE].
B. Basso, L.J. Dixon and G. Papathanasiou, Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 124 (2020) 161603 [arXiv:2001.05460] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 116 (2016) 191602 [arXiv:1512.07912] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps, JHEP 11 (2016) 125 [arXiv:1609.00007] [INSPIRE].
T. Fleury and R. Pereira, Non-planar data of \( \mathcal{N} \) = 4 SYM, JHEP 03 (2020) 003 [arXiv:1910.09428] [INSPIRE].
S.M. Chester, S.S. Pufu and X. Yin, The M-theory S-matrix From ABJM: Beyond 11D Supergravity, JHEP 08 (2018) 115 [arXiv:1804.00949] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, Absence of D4R4 in M-theory From ABJM, JHEP 04 (2020) 052 [arXiv:1808.10554] [INSPIRE].
D.J. Binder, S.M. Chester and S.S. Pufu, AdS4/CFT3 from weak to strong string coupling, JHEP 01 (2020) 034 [arXiv:1906.07195] [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, The M-theory Archipelago, JHEP 02 (2020) 010 [arXiv:1907.13222] [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, 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 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].
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].
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, 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, 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].
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].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
M. Nirschl and H. Osborn, Superconformal Ward identities and their solution, Nucl. Phys. B 711 (2005) 409 [hep-th/0407060] [INSPIRE].
J. Drummond, C. Duhr, B. Eden, P. Heslop, J. Pennington and V.A. Smirnov, Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [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: 2109.08086
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
Dorigoni, D., Green, M.B. & Wen, C. Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2021, 132 (2021). https://doi.org/10.1007/JHEP11(2021)132
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)132