The M-theory dual of a 3 dimensional theory with reduced supersymmetry

TL;DR

This work constructs the M-theory dual of a three-dimensional ${\cal N}=2$ gauge theory obtained by fermion-mass perturbations of the ${\cal N}=8$ M2-brane theory, predicting M2-brane polarization into M5-branes in ${\it AdS}_4\times S^7$. By analyzing both the M5-brane worldvolume actions (PST and PS) and the backreacted warped geometry, it derives a supersymmetric potential with nonzero polarization radii, identifies discrete vacua and their condensates, and explains domain walls as bent M5 configurations. The results provide a coherent holographic picture of vacua structure, domain walls, and condensates in a less-supersymmetric context, and reveal a remarkable relation between M5-brane dynamics and 11D supergravity equations of motion. The approach generalizes to unequal masses and warped multi-shell geometries, offering insights into holographic mechanisms for confinement-like behavior and the spectrum of low-energy excitations in the strongly coupled regime.

Abstract

In a recent paper, Polchinski and Strassler found a string theory dual of a gauge theory with reduced supersymmetry. Motivated by their approach, we perturb the $\N=8$ theory living on a set of N M2 branes to $\N=2$, by adding fermion mass terms. We obtain M-theory duals corresponding to M2 branes polarized into M5 branes, in $AdS_4 \times S_7$. In the course of doing this we come across an interesting feature of the M5 brane action, which we comment on. Depending on the fermion masses we obtain discrete or continuous vacua for our theories. We also obtain dual descriptions for domain walls, instantons and condensates.