Three-Dimensional CFTs and RG Flow from Squashing M2-Brane Horizon

TL;DR

This paper explores how squashing the seven-sphere in M-theory's AdS4 background induces a renormalization group flow between two three-dimensional conformal field theories with different supersymmetry levels, using holographic duality.

Contribution

It provides a concrete example of RG flow between 3D CFTs with different symmetries derived from M-theory backgrounds with squashed spheres, connecting supergravity and field theory insights.

Findings

Identification of UV and IR fixed points with different symmetries

Evidence of RG flow from supergravity scalar potential and domain-wall solutions

Matching conformal dimensions of operators at fixed points

Abstract

Utilizing AdS/CFT correspondence in M-theory, an example of interacting d=3 conformal field theories and renormalization group flow between them is presented. Near-horizon geometry of N coincident M2-branes located on a conical singularity on eight-dimensional hyperk\"ahler manifold or manifold with Spin(7) holonomy is, in large-N limit, AdS4*X7, where X7 is seven-sphere with squashing. Deformation from round $\S_7$ to squashed one is known to lead to spontaneous breaking of N=8 local supersymmetry in gauged AdS4 supergravity to N=1, 0. Via AdS/CFT correspondence, it is interpreted as renormalization group flow from SO(5)*SO(3) symmetric UV fixed point to SO(8) symmetric IR fixed point. Evidences for the interpretation are found both from supergravity scalar potential and existence of interpolating static domain-wall thereof, and from conformal dimensions of relevant chiral primary operator at each fixed point.