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

TL;DR

This paper derives a path integral map between commutative and noncommutative U(1) gauge fields on D-branes in a constant B-field background, clarifying their relationship through boundary state comparisons.

Contribution

It provides a novel path integral formulation linking commutative and noncommutative gauge theories on D-branes, based on boundary state analysis.

Findings

Derived a path integral map between gauge fields

Established correspondence in U(1) gauge theories

Clarified gauge fixing differences on D-branes

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).