A Study of Holographic Renormalization Group Flows in d=6 and d=3

TL;DR

This paper explores holographic RG flows in six-dimensional supergravity, identifying fixed points and vacua, and discusses their physical acceptability and implications for lower-dimensional theories.

Contribution

It provides an explicit analysis of 6D holographic RG flows, including non-supersymmetric and supersymmetric vacua, using the superpotential and Gubser criteria.

Findings

Identification of non-supersymmetric conformal fixed points

Construction of supersymmetric vacua via the superpotential

Application of Gubser criteria to 6D vacua

Abstract

We present an explicit study of the holographic renormalization group (RG) in six dimensions using minimal gauged supergravity. By perturbing the theory with the addition of a relevant operator of dimension four one flows to a non-supersymmetric conformal fixed point. There are also solutions describing non-conformal vacua of the same theory obtained by giving an expectation value to the operator. One such vacuum is supersymmetric and is obtained by using the true superpotential of the theory. We discuss the physical acceptability of these vacua by applying the criteria recently given by Gubser for the four dimensional case and find that those criteria give a clear physical picture in the six dimensional case as well. We use this example to comment on the role of the Hamilton-Jacobi equations in implementing the RG. We conclude with some remarks on AdS_4 and the status of three dimensional superconformal theories from squashed solutions of M-theory.