An N = 2 Supersymmetric Membrane Flow

TL;DR

This paper constructs M-theory solutions representing supersymmetric membrane flows in three dimensions, revealing new IR fixed points and generalizing flows with complex geometries, including del Pezzo and conifold structures.

Contribution

It provides the first explicit M-theory solutions for N=2 supersymmetric membrane flows and introduces a geometric approach to analyze these flows with complex internal manifolds.

Findings

Constructed M-theory solutions dual to supersymmetric flows with mass deformations.

Identified new IR fixed points related to known 3D field theories.

Generalized solutions to include del Pezzo and conifold geometries.

Abstract

We find M-theory solutions that are holographic duals of flows of the maximally supersymmetric N=8 scalar-fermion theory in (2+1) dimensions. In particular, we construct the M-theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M2-brane probes. The (2+1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M-theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geometric manner and use this to obtain an Ansatz for the M-theory flow. We are able to generalize our solution further to obtain flows with del Pezzo sub-manifolds, and we give an explicit solution with a conifold singularity.