Correlators of Giant Gravitons from dual ABJ(M) Theory

TL;DR

This paper extends the study of giant graviton correlators in ABJ(M) theory by computing two-point functions of generalized operators, analyzing their dual gravity states, and exploring effects of non-trivial backgrounds on large N expansions.

Contribution

It introduces generalized Schur polynomial operators in ABJ theory, computes their correlators, and examines non-planar corrections in complex backgrounds, advancing the understanding of gauge/gravity duality.

Findings

Two-point functions computed in free and finite N limits.

Correlators among giant and ordinary gravitons analyzed.

Non-trivial backgrounds modify large N expansion to 1/(N+M) form.

Abstract

We generalize the operators of ABJM theory, given by Schur polynomials, in ABJ theory by computing the two point functions in the free field and at finite $(N_1,N_2)$ limits. These polynomials are then identified with the states of the dual gravity theory. Further, we compute correlators among giant gravitons as well as between giant gravitons and ordinary gravitons through the corresponding correlators of ABJ(M) theory. Finally, we consider a particular non-trivial background produced by an operator with an $\cal R$-charge of $O(N^2)$ and find, in presence of this background, due to the contribution of the non-planar corrections, the large $(N_1,N_2)$ expansion is replaced by $1/(N_1+M)$ and $1/(N_2+M)$ respectively.