Maximal U(1)Y-violating n-point correlators in $$ \mathcal{N} $$ = 4 super-Yang-Mills theory

Abstract

This paper concerns a special class of n-point correlation functions of operators in the stress tensor supermultiplet of $$ \mathcal{N} $$ 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 AdS5× S5 at the same orders as R4, d4R4 and d6R4. 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 AdS5× S5.

Towards the Virasoro-Shapiro amplitude in AdS5×S5

“…A similar property holds for n-point maximally nilpotent correlatorsthose with fermionic degree n − 4 [78][79][80]. These have recently been studied at strong coupling in [57] and one might expect them to be computable from a 10d scalar effective action just as for the four point ones. The next to maximally nilpotent correlators are much more complicated from the point of view of superconformal invariance (for example see [81]).…”

“…Here I is a polynomial in X i and Y i which is a common factor of all interacting 1/2-BPS four-point functions [55]. It is the counterpart of the δ 16 (Q) factor of flat space superamplitudes [57]. We give its explicit form in appendix A.…”

“…The precise definitions of the functions can be found for example in [53]. Furthermore recently in [53,57,68] the corresponding dual (but lowest charge only) correlators were considered and completely fixed via localisation to all orders. This then fixes the remaining ambiguities at this order (assuming B 1 = C 1 = 0 as we discuss around (6.15) and the second bullet point below) in terms of the above functions as…”

Exact properties of an integrated correlator in $$ \mathcal{N} $$ = 4 SU(N) SYM

“…In this section, we will study the large-N expansion with fixed g YM . This is the limit where Yang-Mills instanton contributions are not suppressed, which is crucial for the study of the SL(2, Z) duality of N = 4 SYM (see [5,7,40] for recent results related to this paper). The method we utilised in the previous section is clearly also applicable for this limit.…”

“…The extension to correlators of other operators in the JHEP05(2021)089 stress tensor multiplet also seems feasible. It would similarly be of interest to generalise this construction to n-point correlators that violate the bonus U(1) Y symmetry maximally, that were discussed in [40]. Beyond that, the extension of these ideas to correlators of more general BPS operators appears to be considerably more challenging.…”