Holographic two-point functions of heavy operators revisited

TL;DR

This paper refines the holographic computation of two-point functions for heavy BPS operators in N=4 SYM, introducing boundary terms in the D3-brane action and evaluating boundary contributions in bubbling geometries.

Contribution

It proposes new boundary terms in the D3-brane action for giant gravitons and extends holographic two-point function calculations to complex backgrounds.

Findings

Corrected D3-brane action reproduces gauge theory two-point functions

Boundary terms are essential for a well-defined variational problem

Two-point functions for operators with large scaling dimensions are computed in bubbling geometries

Abstract

In this paper we investigate the holographic computation of the two-point functions of $\frac{1}{2}$-BPS chiral primary operators with scaling dimensions $\Delta \sim N$ or $\Delta \sim N^2$ in $\mathcal{N}=4$ $SU(N)$ SYM using Type IIB supergravity. First we consider giant graviton operators, resolving ambiguities in the previous literature on holographic computation of the two-point function, and make a new proposal for this calculation. We argue that the D3-brane action for the giant gravitons (as well as for their $\frac{1}{4}$- and $\frac{1}{8}$-BPS counterparts) should contain additional boundary terms which arise naturally from the path integral and which are required to make the variational problem well-defined. We derive the form of these terms and show that the corrected action has an on-shell value that reproduces the two-point function of the gauge theory operators. Then we consider operators with $\Delta \sim N^2$ and calculate the two-point function by evaluating the Gibbons-Hawking-York boundary term in the Type IIB pseudo-action in the Lin-Lunin-Maldacena bubbling geometry background.