Moduli and BPS configurations of the BLG theory

TL;DR

This paper investigates how background four-form fields affect the moduli space of BPS configurations in the BLG theory, revealing reductions in moduli space dimensions and providing explicit solutions with specific symmetries.

Contribution

It provides a detailed analysis of the moduli space of the BLG theory with background fields and constructs explicit BPS solutions demonstrating symmetry reductions.

Findings

Moduli space is 16-dimensional without four-form field

Presence of four-form field reduces the moduli space dimension

Constructed explicit BPS solution with specific symmetries

Abstract

We study the moduli space of scalars in the BLG theory with and without a constant background four-form field. The classical vacuum moduli space is sixteen-dimensional in the absence of the four-form field. In its presence, however, the moduli space of BPS configurations may be reduced in dimension. We exemplify this with a BPS configuration having $SO(1,2)$ world-volume symmetry and $SO(4) \times SO(4)$ R-symmetry in the presence of a four-form field, by constructing an explicit solution.