Maximal U(1) Y -violating n-point correlators in N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory - Michael B. Green; Congkao Wen (Journal of High Energy Physics, 2021)
Abstract This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of N $$ \mathcal{N} $$ = 4 supersymmetric SU(N) Yang-Mills theory. These are “maximal U(1) Y -violating” correlators that violate the bonus U(1) Y charge by a maximum of 2(n − 4) units. We will demonstrate that such correlators satisfy SL(2, ℤ)-covariant recursion relations that relate n-point correlators to (n − 1)-point correlators in a manner analogous to the soft dilaton relations that relate the corresponding amplitudes in flat-space type IIB superstring theory. These recursion relations are used to determine terms in the large-N expansion of n-point maximal U(1) Y -violating correlators in the chiral sector, including correlators with four superconformal stress tensor primaries and (n − 4) chiral Lagrangian operators, starting from known properties of the n = 4 case. We concentrate on the first three orders in 1/N beyond the supergravity limit. The Mellin representations of the correlators are polynomials in Mellin variables, which correspond to higher derivative contact terms in the low-energy expansion of type IIB superstring theory in AdS 5 × S 5 at the same orders as R 4 , d 4 R 4 and d 6 R 4. The coupling constant dependence of these terms is found to be described by non-holomorphic modular forms with holomorphic and anti-holomorphic weights (n − 4, 4 − n) that are SL(2, ℤ)-covariant derivatives of Eisenstein series and certain generalisations. This determines a number of non-leading contributions to U(1) Y -violating n-particle interactions (n > 4) in the low-energy expansion of type IIB superstring amplitudes in AdS 5 × S 5.