Derivative corrections to Dirac-Born-Infeld Lagrangian and non-commutative gauge theory

TL;DR

This paper derives the most general form of two-derivative corrections to the Dirac-Born-Infeld Lagrangian consistent with the equivalence between ordinary and non-commutative gauge theories on D-branes with a constant B field.

Contribution

It constructs the complete set of two-derivative corrections to the DBI Lagrangian up to quartic order, satisfying the gauge equivalence constraints.

Findings

Derived the general form of two-derivative corrections up to quartic order.

Confirmed consistency with gauge equivalence between ordinary and non-commutative descriptions.

Provided explicit constraints on the effective Lagrangian.

Abstract

We consider the constraints on the effective Lagrangian of the rank-one gauge field on D-branes imposed by the equivalence between the description by ordinary gauge theory and that by non-commutative gauge theory in the presence of a constant B field. It is shown that we can consistently construct the two-derivative corrections to the Dirac-Born-Infeld Lagrangian up to the quartic order of field strength and the most general form which satisfies the constraints up to this order is derived.