Vacuum Condensates on the Coulomb Branch

TL;DR

This paper investigates correlation functions on the Coulomb branch of planar $ 4$ SYM, revealing their integrability, OPE properties, and holographic duals, and introduces a nonperturbative formula linking Coulomb branch and large charge correlators.

Contribution

It provides a new nonperturbative formula connecting Coulomb branch correlators with large charge insertions and extends the large charge-Coulomb branch connection to the large N limit.

Findings

One-point functions computed at weak coupling with a spin-chain representation.

Two-point functions of chiral primaries have an infinite OPE radius of convergence.

A holographic interpretation involving a large D3-brane in AdS is proposed.

Abstract

We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and holography. First, we compute one-point functions of arbitrary scalar operators at weak coupling and derive a compact spin-chain representation. We next study the two-point functions of chiral primaries at one loop and find that the radius of convergence of OPE in position space is infinite. We estimate the asymptotic growth of the OPE data based on this finding. Finally, we propose a concrete nonperturbative formula that connects the correlation functions on the Coulomb branch with the correlation functions with large charge insertions at the conformal point and provide a holographic interpretation based on a large D3-brane in AdS. The formula extends the known connection between the large charge sector and the Coulomb branch for rank-1 theories to the large $N$ limit.