Holographic Coulomb branch vevs

TL;DR

The paper provides a comprehensive holographic computation of the Coulomb-branch vevs in N=4 SYM for general D3-brane distributions, establishing exact agreement with field theory across all chiral primaries via a ten-dimensional to five-dimensional map. By expanding the harmonic function that encodes the CB geometry and relating its coefficients to chiral primary vevs, it demonstrates a robust method to extract gauge-invariant vevs from asymptotically AdS geometries. A key result is that, under a linearized treatment, the vevs are given by a universal integral of the eigenvalue distribution against SO(6) harmonics, matching field theory after a coupling-rescaling, with cancellations argued for higher-order terms in specific cases. The work further explores non-normalizable deformations corresponding to half-supersymmetric irrelevant operators, and conjectures gravity duals for a broader class of 16-supercharge deformations, extending holography beyond strictly AdS5×S^5 backgrounds.

Abstract

We compute holographically the vevs of all chiral primary operators for supergravity solutions corresponding to the Coulomb branch of N=4 SYM and find exact agreement with the corresponding field theory computation. Using the dictionary between 10d geometries and field theory developed to extract these vevs, we propose a gravity dual of a half supersymmetric deformation of N=4 SYM by certain irrelevant operators.