TY - JOUR

T1 - Modular invariance in superstring theory from N = 4 super-Yang-Mills

AU - Chester, Shai M.

AU - Green, Michael B.

AU - Pufu, Silviu S.

AU - Wang, Yifan

AU - Wen, Congkao

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/11

Y1 - 2020/11

N2 - We study the four-point function of the lowest-lying half-BPS operators in the N = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed N = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N2− 1 and are independent of τ and τ¯ , we find that the terms of order N and 1/N in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series E(32ττ¯) and E(52ττ¯), respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R4 and D4R4 contact inter-actions, which, for the R4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order N12−m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant.

AB - We study the four-point function of the lowest-lying half-BPS operators in the N = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed N = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N2− 1 and are independent of τ and τ¯ , we find that the terms of order N and 1/N in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series E(32ττ¯) and E(52ττ¯), respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R4 and D4R4 contact inter-actions, which, for the R4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order N12−m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant.

KW - 1/N Expansion

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

KW - Scattering Amplitudes

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U2 - 10.1007/JHEP11(2020)016

DO - 10.1007/JHEP11(2020)016

M3 - Article

AN - SCOPUS:85095697118

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 11

M1 - 16

ER -