An N=2 gauge theory and its supergravity dual

TL;DR

The paper analyzes holographic flows on the scalar manifold of $5$-dimensional $\mathcal{N}=8$ gauged supergravity that correspond to mass deformations of $\mathcal{N}=4$ SYM, focusing on a mass term for the adjoint hypermultiplet that yields an $\mathcal{N}=2$ theory. An exact $5$-D solution is obtained and uplifted to a type-IIB background, enabling a holographic study of operator spectra and Wilson loops; the flows are controlled by a single non-positive constant $c$, describing part of the $\mathcal{N}=2$ Coulomb branch at strong coupling. A criterion to distinguish physical from unphysical curvature singularities is proposed and tested against field theory expectations, with consistency across several backgrounds. The work provides a concrete holographic realization of $\mathcal{N}=2$ deformations of $\mathcal{N}=4$ SYM, clarifying screening properties and the role of singularities in the gravity dual.

Abstract

We study flows on the scalar manifold of N=8 gauged supergravity in five dimensions which are dual to certain mass deformations of N=4 super Yang--Mills theory. In particular, we consider a perturbation of the gauge theory by a mass term for the adjoint hyper-multiplet, giving rise to an N=2 theory. The exact solution of the 5-dim gauged supergravity equations of motion is found and the metric is uplifted to a ten-dimensional background of type-IIB supergravity. Using these geometric data and the AdS/CFT correspondence we analyze the spectra of certain operators as well as Wilson loops on the dual gauge theory side. The physical flows are parametrized by a single non-positive constant and describe part of the Coulomb branch of the N=2 theory at strong coupling. We also propose a general criterion to distinguish between `physical' and `unphysical' curvature singularities. Applying it in many backgrounds arising within the AdS/CFT correspondence we find results that are in complete agreement with field theory expectations.

Figures (1)

• Figure 1: This figure shows the different behaviours of the function $e^{\sqrt{6} \alpha_2}$ as a function of $\alpha_3$ using (\ref{['scasol']}). For $c<0$, it decreases monotonously to zero at a finite value $\alpha_3^{\rm max}$. For $c=0$ (the dashed curve) the same minimum at zero is attained, but for $\alpha_3\to \infty$. In contrast, for $c>0$ the function first reaches a minimum, at a finite value $\alpha_3^{\rm min}$, before it runs off to infinity at $\alpha_3\to \infty$.