Squashing Gravity Dual of N=6 Superconformal Chern-Simons Gauge Theory

TL;DR

This paper derives field equations for perturbations in eleven-dimensional supergravity related to a specific geometric setup and analyzes the holographic RG flow between fixed points in dual superconformal Chern-Simons theories.

Contribution

It provides new four-dimensional field equations for perturbations of the quotient seven-sphere and explores the holographic RG flow between different superconformal fixed points.

Findings

Derived supergravity scalar potential and RG flow equations.

Identified dual operators in boundary theories.

Mapped UV and IR fixed points in the dual Chern-Simons theories.

Abstract

Four-dimensional field equations are determined for perturbations of the quotient seven-sphere size and squashing parameter in eleven-dimensional supergravity. The quotient seven-sphere is a S^1-bundle over the CP^3 which is regarded as a S^2-fibration over the base S^4. By analyzing the AdS_4 supergravity scalar potential, the holographic supersymmetric(or nonsupersymmetric) renormalization group(RG) flow from N=1(or N=0) SO(5) x U(1)-invariant UV fixed point to N=6(or N=0) SU(4)_R x U(1)-invariant IR fixed point is obtained. The three-dimensional boundary theories are described by superconformal Chern-Simons matter theories and a dual operator corresponding to this RG flow is described.