Generating functions for giant graviton bound states

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 $$ \frac{1}{N} $$ 1 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.

Multi-matrix correlators and localization

“…One might be able to explicitly compute Lefshetz thimbles for this case and determine whether localization fails or not, or whether complex saddle points are needed. It would be interesting to construct multi-matrix analogues of the generating functions found in [21] for determinant operators. This would help in constructing the precise operators dual to intersecting giants [52], and particularly in understanding their integrable boundary states [53].…”

“…An explicit mapping between BPS states made out of more than one matrix and asymptotically AdS 5 × S 5 geometries is still lacking, though a compelling description in terms of bubbling geometries seems to exist [18][19][20]. The study of generating functions for multi-matrix correlators was outlined in [10,21] for certain classes of operators, and more…”