New Two Dimensional Massless Field Theory from Bagger-Lambert-Gustavsson Model

TL;DR

This paper derives a new two-dimensional massless field theory from the Bagger-Lambert-Gustavsson model via compactification, revealing a connection to a supersymmetric Lie 3-algebra generalization of the Green-Schwarz superstring.

Contribution

It introduces a novel 2D massless field theory from BLG model compactification, extending the Green-Schwarz superstring with Lie 3-algebra structures.

Findings

The theory is coupled with SO(1,1) scalar and vector fields.

In the limit g_{BLG} → ∞, it reduces to a supersymmetric Lie 3-algebra generalization of the superstring.

The fields are valued in the Lie 3-algebra and its endomorphisms.

Abstract

By compactifying the Bagger-Lambert-Gustavsson model on $\mathbb{R}^{1,1} \times S^1$, we obtain a new two dimensional massless field theory with dynamical fields valued in the Lie 3-algebra $\mathcal{A}$ coupled with an SO(1,1) scalar and vector field which are valued in the set $End(\mathcal{A})$ of the endomorphisms of the Lie 3-algebra. In the limit $g_{BLG} \to \infty$ the theory reduces to a supersymmetric Lie 3-valued generalization of the Green-Schwarz superstring in the light-cone gauge.