## 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 AdS_{5}× S^{5}.

Original language | English (US) |
---|---|

Article number | 212 |

Journal | Journal of High Energy Physics |

Volume | 2021 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2021 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- 1/N Expansion
- AdS-CFT Correspondence
- Conformal Field Theory
- Scattering Amplitudes