A Study of a Non-Abelian Generalization of the Born-Infeld Action

TL;DR

This paper proposes a novel non-Abelian extension of the Born-Infeld action that maintains Lorentz and gauge invariance, incorporating stringy corrections and revealing instanton-like solutions in the SU(2) case.

Contribution

It introduces a new non-Abelian Born-Infeld action combining spacetime and group indices, with solutions demonstrating instanton-like configurations.

Findings

The action is Lorentz and gauge invariant.

The power expansion includes Yang-Mills and stringy correction terms.

Existence of instanton-like solutions with finite action.

Abstract

A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order term is the Yang-Mills action and the second term corresponds to the bosonic stringy correction to this action. Solutions of the Euler-Lagrange equation for the SU(2) case are considered and we show that there exists an instanton-like solution which has winding number one and finite action.