Supersymmetric Non-Abelian Born-Infeld Theory

TL;DR

This paper demonstrates that symmetric trace is essential in constructing a supersymmetric non-Abelian Born-Infeld theory that reproduces the bosonic Dirac-Born-Infeld structure, and explores BPS relations within this framework.

Contribution

It introduces a superfield construction using curvature invariants and establishes the necessity of symmetric trace for the correct bosonic limit.

Findings

Symmetric trace is mandatory for the non-Abelian Born-Infeld structure.

The superfield approach reproduces the bosonic Dirac-Born-Infeld Lagrangian.

Connections between BPS relations and supersymmetry are discussed.

Abstract

Using the natural curvature invariants as building blocks in a superfield construction, we show that the use of a symmetric trace is mandatory if one is to reproduce the square root structure of the non-Abelian Dirac-Born-Infeld Lagrangian in the bosonic sector. We also discuss the BPS relations in connection with our supersymmetry construction.