Constraints on effective Lagrangian of D-branes from non-commutative gauge theory

TL;DR

This paper resolves a discrepancy between non-commutative and ordinary gauge theories describing D-brane dynamics by introducing B-dependent correction terms, establishing a systematic method to constrain the effective Lagrangian.

Contribution

It introduces gauge-invariant B-dependent correction terms in the field redefinition, resolving previous incompatibilities and providing a systematic approach to derive constraints on the effective Lagrangian.

Findings

Compatibility of descriptions requires B-dependent metric corrections.

Systematic method established for alpha' expansion constraints.

Resolved previous incompatibility in bosonic string theory context.

Abstract

It was argued that there are two different descriptions of the effective Lagrangian of gauge fields on D-branes by non-commutative gauge theory and by ordinary gauge theory in the presence of a constant B field background. In the case of bosonic string theory, however, it was found in the previous works that the two descriptions are incompatible under the field redefinition which relates the non-commutative gauge field to the ordinary one found by Seiberg and Witten. In this paper we resolve this puzzle to observe the necessity of gauge-invariant but B-dependent correction terms involving metric in the field redefinition which have not been considered before. With the problem resolved, we establish a systematic method under the alpha' expansion to derive the constraints on the effective Lagrangian imposed by the compatibility of the two descriptions where the form of the field redefinition is not assumed.