Domain Walls in Noncommutative Field Theories

TL;DR

This paper investigates static kink solutions in noncommutative field theories, revealing complex structures like BPS kinks and tensionless half-kinks, and explores their interpretation as D-branes with induced fundamental string charge.

Contribution

It provides a detailed analysis of kink solutions in NC tachyon actions, including the effects of NC gauge fields, and interprets these solutions as D-branes with additional string charges.

Findings

Discovery of rich static kink structures in NC theories.

Identification of BPS and tensionless half-kink solutions.

Demonstration of induced fundamental string charge via NC gauge fields.

Abstract

We study kinks in a wide class of noncommutative (NC) field theories. We find rich structure of the static kinks in DBI type NC tachyon action for an unstable D$p$-brane with general constant open string metric and NC parameter. Among which thick topological BPS NC kink and tensionless half-kink are particularly intriguing. Reproduction of the correct decent relation between D$p$ and D$(p-1)$ lets us interpret the obtained NC kinks as codimension-one D-brane and its composites. If we turn on DBI type NC U(1) gauge field on an unstable D2-brane, only constant field strength is allowed by gauge equation and NC Bianchi identity. Inclusion of the NC U(1) gauge field induces fundamental string charge localized on the codimension-one brane, which turns D$(p-1)$ into D$(p-1)$F1.