Non-commutative vs. Commutative Descriptions of D-brane BIons

TL;DR

This paper demonstrates the exact non-perturbative mapping between non-commutative and commutative descriptions of D-brane BIons, supporting their fundamental equivalence in string theory.

Contribution

It provides an exact non-perturbative mapping of BIon solutions between non-commutative and ordinary gauge theories on D-branes, confirming their equivalence.

Findings

Exact non-perturbative mapping of solutions

Supports equivalence of non-commutative and commutative descriptions

BIon solutions saturate BPS bounds in both frameworks

Abstract

The U(1) gauge theory on a D3-brane with non-commutative worldvolume is shown to admit BIon-like solutions which saturate a BPS bound on the energy. The mapping of these solutions to ordinary fields is found exactly, namely non-perturbatively in the non-commutativity parameters. The result is precisely an ordinary supersymmetric BIon in the presence of a background B-field. We argue that the result provides evidence in favour of the exact equivalence of the non-commutative and the ordinary descriptions of D-branes.