Current correlators in the Coulomb branch of N=4 SYM

TL;DR

This paper investigates R-symmetry current correlators in the Coulomb branch of N=4 SYM using AdS/CFT, revealing a universal behavior of 2-point functions and mapping the spectrum problem to supersymmetric quantum mechanics.

Contribution

It demonstrates the universality of 2-point functions across broken and unbroken symmetries and connects the spectrum analysis to supersymmetric quantum mechanics.

Findings

All 2-point functions fall into the same universality class.

Spectrum analysis reduces to a supersymmetric quantum mechanics problem.

Explicit computations for specific examples confirm the theoretical predictions.

Abstract

We study correlators of R-symmetry currents in the Coulomb branch of N = 4 supersymmetric gauge theory in the large-N limit, using the AdS/CFT correspondence. In particular, we consider gauge fields in the presence of gravity and scalar fields parameterizing the coset SL(6,R)/SO(6) in the context of five-dimensional gauged supergravity. From a ten-dimensional point of view these backgrounds correspond to continuous D3-brane distributions. We find the surprising result that all 2-point functions of gauge currents fall into the same universality class, irrespectively of whether they correspond to broken or unbroken symmetries. We show that the problem of finding the spectrum can be mapped into an equivalent Schroedinger problem for supersymmetric quantum mechanics. The corresponding potential is the supersymmetric partner of the potential arising in studies of the spectrum for massless scalars and transverse graviton fluctuations in these backgrounds and the associated spectra are also identical. We discuss in detail two examples where these computations can be done explicitly as in the conformal case.