Holographic RG flows in N=3 Chern-Simons-Matter theory from N=3 4D gauged supergravity

TL;DR

This paper explores supersymmetric renormalization group flows in three-dimensional N=3 Chern-Simons-Matter theory using four-dimensional gauged supergravity, identifying new critical points and explicit flow solutions.

Contribution

It presents the discovery of a new supersymmetric AdS4 critical point with reduced symmetry and provides explicit analytic RG flow solutions connecting different critical points.

Findings

Identified a new N=3 supersymmetric AdS4 critical point with unbroken SO(3)×U(1) symmetry.

Constructed explicit analytic RG flow solutions between critical points.

Found supersymmetric AdS2 solutions with various symmetry groups.

Abstract

We study various supersymmetric RG flows of $N=3$ Chern-Simons-Matter theory in three dimensions by using four-dimensional $N=3$ gauged supergravity coupled to eight vector multiplets with $SO(3)\times SU(3)$ gauge group. The $AdS_4$ critical point preserving the full $SO(3)\times SU(3)$ provides a gravity dual of $N=3$ superconformal field theory with flavor symmetry $SU(3)$. We study the scalar potential and identify a new supersymmetric $AdS_4$ critical point preserving the full $N=3$ supersymmetry and unbroken $SO(3)\times U(1)$ symmetry. An analytic RG flow solution interpolating between $SO(3)\times SU(3)$ and $SO(3)\times U(1)$ critical points is explicitly given. We then investigate possible RG flows from these $AdS_4$ critical points to non-conformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form $AdS_2\times \Sigma_2$ with $\Sigma_2$ being a two-sphere or a two-dimensional hyperbolic space and find a number of $AdS_2$ geometries preserving four supercharges with $SO(2)\times SO(2)\times SO(2)$ and $SO(2)\times SO(2)$ symmetries.