Generating Functions for Giant Graviton Bound States

TL;DR

This paper introduces a new integral-based generating function approach for constructing operators dual to giant graviton bound states with open strings, enabling systematic analysis beyond the planar limit.

Contribution

It provides a novel integral representation for Gauss graph operators, facilitating systematic ${1ackslash N}$ expansions and analysis of the dilatation operator's action.

Findings

Constructed integral generating functions for giant graviton operators

Simplified the construction of Gauss graph operators

Enabled systematic ${1ackslash N}$ expansion and analysis

Abstract

We construct generating functions for operators dual to systems of giant gravitons with open strings attached. These operators have a bare dimension of order $N$ so that the usual methods used to solve the planar limit are not applicable. The generating functions are given as integrals over auxiliary variables, which implement symmetrization and antisymmetrization of the indices of the fields from which the operator is composed. Operators of a good scaling dimension (eigenstates of the dilatation operator) are known as Gauss graph operators. Our generating functions give a simple construction of the Gauss graph operators which were previously obtained using a Fourier transform on a double coset. The new description provides a natural starting point for a systematic ${1\over N}$ expansion for these operators as well as the action of the dilatation operator on them, in terms of a saddle point evaluation of their integral representation.