Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Holographic two-point functions of heavy operators revisited

Prokopii Anempodistov

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 $Δ\sim N$ or $Δ\sim N^2$ 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 $Δ\sim N^2$ 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.

Holographic two-point functions of heavy operators revisited

Abstract

In this paper we investigate the holographic computation of the two-point functions of -BPS chiral primary operators with scaling dimensions or in 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 - and -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 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.

Paper Structure

This paper contains 8 sections, 75 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Giant graviton and dual giant graviton two-point functions
  3. Giant gravitons in $S^3 \subset S^5$ and derivation of the boundary terms
  4. Generalization to dual giant gravitons in $S^3 \subset AdS_5$ and $\frac{1}{4}$- and $\frac{1}{8}$-BPS cases
  5. LLM two-point functions
  6. Conclusions
  7. Review of the giant graviton two-point function calculation in the previous literature
  8. Asymptotic expansions

Figures (2)

  • Figure 1: The giant graviton profile in the global $AdS$ (left) and the same profile in the Poincaré coordinates (right). We emphasize here that the $\rho=0$ worldline in the global coordinates translates into the semicircular geodesic when translated into Poincaré, and the cutoffs at $z=\epsilon$ are naturally translated into cutoffs for the global time.
  • Figure 2: The dual giant graviton profile in the Poincaré coordinates.