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- Title
New modular invariants in N = 4 Super-Yang-Mills theory.
- Authors
Chester, Shai M.; Green, Michael B.; Pufu, Silviu S.; Wang, Yifan; Wen, Congkao
- Abstract
We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ, τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain "generalized Eisenstein series" which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.
- Subjects
PARTITION functions; MODULAR functions; SUPERSTRING theories; EIGENVALUE equations; STRAINS &; stresses (Mechanics); EISENSTEIN series
- Publication
Journal of High Energy Physics, 2021, Vol 2021, Issue 4, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP04(2021)212