A Path Integral Representation of the Map between Commutative and Noncommutative Gauge Fields

Abstract

The world-volume theory on a D-brane in a constant B-field background can be described by either commutative or noncommutative Yang-Mills theories. These two descriptions correspond to two different gauge fixing of the diffeomorphism on the brane. Comparing the boundary states in the two gauges, we derive a map between commutative and noncommutative gauge fields in a path integral form, when the gauge group is U(1).Comment: 14 pages, harvmac; transformation of Wilson loop corrected, SW map at the 2nd order correcte