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Unmixing Supergravity

F. Aprile, J. M. Drummond, P. Heslop, H. Paul

TL;DR

The paper addresses degeneracy in the double-trace spectrum of N=4 SYM at large N by resolving mixing between free-field and tree-level supergravity contributions using four-point functions of half-BPS operators. It employs a combination of Mellin-space tree-level supergravity, GL(2|2) superconformal blocks, and a novel bosonised approach to derive a remarkably simple structure for anomalous dimensions and OPE coefficients, including closed-form expressions for representations [n,0,n]. The resulting framework yields negative anomalous dimensions with a universal, orthogonal mixing matrix tilde{c}, enabling predictions for leading O(1/N^2) data and informing potential higher-loop corrections. The work clarifies the large-N holographic spectrum, provides a practical method to extract strong-coupling data from correlators, and suggests broader applicability to other holographic CFTs with KK towers of KK modes on S^5.

Abstract

We examine the double-trace spectrum of $\mathcal{N} = 4$ super Yang-Mills theory in the supergravity limit. At large $N$ double-trace operators exhibit degeneracy. By considering free-field and tree-level supergravity contributions to four-point functions of half-BPS operators we resolve the degeneracy for a large family of double-trace operators. The mixing problem reveals a surprisingly simple structure which allows us to obtain their three-point functions at leading order in the large $N$ expansion as well as their leading anomalous dimensions.

Unmixing Supergravity

TL;DR

The paper addresses degeneracy in the double-trace spectrum of N=4 SYM at large N by resolving mixing between free-field and tree-level supergravity contributions using four-point functions of half-BPS operators. It employs a combination of Mellin-space tree-level supergravity, GL(2|2) superconformal blocks, and a novel bosonised approach to derive a remarkably simple structure for anomalous dimensions and OPE coefficients, including closed-form expressions for representations [n,0,n]. The resulting framework yields negative anomalous dimensions with a universal, orthogonal mixing matrix tilde{c}, enabling predictions for leading O(1/N^2) data and informing potential higher-loop corrections. The work clarifies the large-N holographic spectrum, provides a practical method to extract strong-coupling data from correlators, and suggests broader applicability to other holographic CFTs with KK towers of KK modes on S^5.

Abstract

We examine the double-trace spectrum of super Yang-Mills theory in the supergravity limit. At large double-trace operators exhibit degeneracy. By considering free-field and tree-level supergravity contributions to four-point functions of half-BPS operators we resolve the degeneracy for a large family of double-trace operators. The mixing problem reveals a surprisingly simple structure which allows us to obtain their three-point functions at leading order in the large expansion as well as their leading anomalous dimensions.

Paper Structure

This paper contains 19 sections, 165 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM
  3. Large-N correlation functions at strong 't Hooft coupling
  4. Tree-Level Supergravity from Mellin space
  5. $\mathcal{N}=4$ superconformal OPE
  6. $GL(2|2)$ superconformal partial wave
  7. Explicit form of the long $\mathcal{N}=4$ superconformal blocks.
  8. Bosonised superblocks
  9. Free theory and Long-multiplet spectrum
  10. Determining strong coupling data from the correlator
  11. Twist 4
  12. Twist 6
  13. General twist
  14. Generalisation from $[0,0,0]$ to $[n,0,n]$ representations
  15. [1,0,1]
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Varying $t$ we show on a log-log plot the value of the dimension $\Delta^\star_l$ at the crossing point $\Delta^{[0,0,0]}_{t+1,l,1} - \Delta^{[0,0,0]}_{t,l,t-1}=0$ as function of ${1}/{N^2}$ for $l=0$ (red), $l=2$ (blue) and $l=4$ (green). The best fit given by the solid black line is $\Delta^\star\approx u_l /N^{1/4}$ with $u_{l=0,2,4}\approx\{4,6.3,8\}$.