On the non-abelian Born-Infeld action

TL;DR

The paper tackles the problem of generalizing the Dirac-Born-Infeld action to non-abelian gauge groups, where noncommuting field strengths create ambiguities that Tseytlin's symmetrized-trace prescription partially addresses but fails at $F^6$ order. It combines string-theory constraints from constant-background spectra (and Hashimoto-Taylor analyses) with a controlled inclusion of commutator terms, aided by a diagrammatic counting method to organize higher-order invariants. The main contribution is showing that specific commutator contractions must be added to the symmetrized-trace action to reproduce the string-theory spectrum at $({\alpha'})^6$, while self-dual backgrounds reduce to linear Yang-Mills; the work also discusses possible fermionic terms and the Seiberg-Witten non-commutative duality. These insights advance a consistent non-abelian D-brane effective action and illuminate connections to non-commutative gauge theories and D-brane dynamics.

Abstract

We discuss some aspects of the generalization of the Born-Infeld action to non-abelian gauge groups and show how the discrepancy between Tseytlin's symmetrized trace proposal and string theory can be corrected at order $F^6$. We also comment on the possible quadratic order fermionic terms.

Figures (2)

• Figure 1. 1: Diagramatic representation of $3 \ {\mathbf {STr}} ({\mathbf F}^4)$.
• Figure 1. 2: Relation between diagrams for $F=\ ^\star F$.