Instantons in the U(1) Born-Infeld Theory and Noncommutative Gauge Theory

TL;DR

This paper derives a BPS bound for four-dimensional U(1) Born-Infeld theory with a constant B field, finding explicit instanton-like solutions that relate to noncommutative gauge theory and D-brane configurations.

Contribution

It introduces a BPS bound and explicit instanton solutions in U(1) Born-Infeld theory, connecting them to noncommutative gauge theories and D-brane physics.

Findings

Explicit BPS solutions with finite action proportional to instanton number.

Solutions represent D(p-4)-branes within Dp-branes, despite singularities.

Discussion of relations to noncommutative U(1) instantons.

Abstract

We derive a BPS-type bound for four-dimensional Born-Infeld action with constant B field background. The supersymmetric configuration saturates this bound and is regarded as an analog of instanton in U(1) gauge theory. Furthermore, we find the explicit solutions of this BPS condition. These solutions have a finite action proportional to the instanton number and represent D(p-4)-branes within a Dp-brane although they have a singularity at the origin. Some relations to the noncommutative U(1) instanton are discussed.