Three-dimensional CFTs and RG flow from squashing M2-brane horizon

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 hyper-Kähler manifold or manifold with Spin(7) holonomy is, in large-N limit, AdS₄ × X₇, where X₇ is seven-sphere with squashing. Deformation from round S₇ to squashed one is known to lead to spontaneous breaking of script N = 8 local supersymmetry in gauged AdS₄ supergravity to script 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. Evidence for the interpretation is found both from the supergravity scalar potential and from the existence of interpolating static domain-wall thereof, and from the conformal dimensions of the relevant chiral primary operator at each fixed point.