More CFTs and RG Flows from Deforming M2/M5-Brane Horizon

TL;DR

This paper explores how deforming the near-horizon geometries of M2 and M5 branes leads to new renormalization group flows between different superconformal fixed points, revealing rich structures in M-theory compactifications.

Contribution

It identifies new RG flows from deformations of M2 and M5-brane geometries, including flows between supersymmetric fixed points and non-supersymmetric ones, extending previous analyses.

Findings

Deformation of X7 leads to RG flow between N=(0,1) and N=(3,0) fixed points.

No nontrivial RG flows found for certain internal manifolds like SO(5)/SO(3)_{max}.

Deformation of S7 induces flow from N=8 to N=1 G_2 invariant fixed point.

Abstract

Near-horizon geometry of coincident M2-branes at a conical singularity is related to M-theory on AdS4 times an appropriate seven-dimensional manifold X7. For X_7=N^{0,1,0}, squashing deformation is known to lead to spontaneous (super) symmetry breaking from N=(3, 0) to N=(0, 1) in gauged AdS4 supergravity. Via AdS/CFT correspondence, it is interpreted as renormalization group flow of strongly coupled three-dimensional field theory with SU(3)*SU(2) global symmetry. The flow interpolates between N=(0,1) fixed point in the UV to N=(3,0)fixed point in the IR. Evidences for the interpretation are found both from critical points of the supergravity scalar potential and from conformal dimension of relevant chiral primary operators at each fixed point. We also analyze cases with X7=SO(5)/SO(3)_{max}, V_{5,2}(R), M^{1,1,1}, Q^{1,1,1} and find that there is no nontrivial renormalization group flows. We extend the analysis to Englert type vacua of M-theory. By analyzing de Wit-Nicolai potential, we find that deformation of S7 gives rise to renormalization group flow from N=8, SO(8) invariant UV fixed point to N=1, G_2 invariant IR fixed point. For AdS_7 supergravity relevant for near-horizon geometry of coincident M5-branes, we also point out a nontrivial renormalization group flow from N=1 superconformal UV fixed point to non-supersymmetric IR fixed point.