Flowing to $\mathcal{N}=3$ Chern--Simons-matter theory

TL;DR

This paper constructs holographic RG flows in 3D Chern--Simons theories, showing how they connect different supersymmetric fixed points, including an IR $ ext{N}=3$ CFT, via domain-wall solutions in supergravity.

Contribution

It introduces new holographic RG flows with $ ext{N}=3$ supersymmetry, linking UV and IR fixed points with different symmetries and supersymmetries, via explicit supergravity solutions.

Findings

Identification of IR $ ext{N}=3$ fixed point with $ ext{SU}(2)$ symmetry.

Construction of domain-wall solutions in gauged supergravity.

Explicit RG flow from $ ext{N}=2$ to $ ext{N}=3$ CFTs.

Abstract

New renormalisation group flows of three-dimensional Chern--Simons theories with a single gauge group $\textrm{SU}(N)$ and adjoint matter are found holographically. These RG flows have an infrared fixed point given by a CFT with $\mathcal{N}=3$ supersymmetry and $\text{SU}(2)$ flavour symmetry. The ultraviolet fixed point is again described by a CFT with either $\mathcal{N}=2$ and $\text{SU}(3)$ symmetry or $\mathcal{N}=1$ and $\text{G}_{2}$ symmetry. The gauge/gravity duals of these RG flows are constructed as domain-wall solutions of a gauged supergravity model in four dimensions that enjoys an embedding into massive IIA supergravity. A concrete RG flow that brings a mass deformation of the $\mathcal{N}=2$ CFT into the $\mathcal{N}=3$ CFT at low energies is described in detail.