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

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.

39 pages, LaTeX2e, no figures; v2: Appendix B corrected, minor changes; v3: Abstract, Introduction and Section 5 revised to emphasize our new results, minor changes, references updated, version to be published in Nucl. Phys. B

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• Comments on Gauge Equivalence in Noncommutative Geometry
• Derivative corrections to Dirac-Born-Infeld Lagrangian and non-commutative gauge theory
• A Path Integral Representation of the Map between Commutative and Noncommutative Gauge Fields
• On the Equivalence between Noncommutative and Ordinary Gauge Theories
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• Open-String Actions and Noncommutativity Beyond the Large-B Limit
• Relations between Non-Commutative and Commutative Spacetime