Mass-Deformed Bagger-Lambert Theory and its BPS Objects

TL;DR

The work constructs a mass-deformed Bagger-Lambert theory with $16$ supersymmetries and $SO(4)\times SO(4)$ R-symmetry, in which the R-charge appears as a non-central term in the superalgebra. It analyzes the vacuum structure—one symmetric vacuum and two inequivalent broken sectors—and derives $1/2$ BPS domain walls between the symmetric and broken phases, along with $1/4$ BPS, supertube-like solitons (q-balls and vortices) that exhibit fractional spin due to the Chern-Simons term. The $1/4$ BPS equations reduce to abelian Chern-Simons-Higgs-type relations, and large-charge limits recover supertube physics, including domain walls binding R-charges and momentum. The paper also discusses mass deformations that reduce supersymmetry and their impact on the soliton spectrum, providing a concrete 3D CS-matter realization with non-central charges relevant to M2–M5 polarization phenomena.

Abstract

We find a sixteen supersymmetric mass-deformed Bagger-Lambert theory with $SO(4)\times SO(4)$ global R-symmetry. The R-charge plays the `non-central' term in the superalgebra. This theory has one symmetric vacuum and two in-equivalent broken sectors of vacua. Each sector of the broken symmetry has the SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric phase and any broken phase, and 1/4 BPS supertube-like objects, which may appear as anyonic q-balls in the symmetric phase or vortices in the broken phase. We also discuss mass deformations which reduces the number of supersymmetries.