Quasi-localized states on noncommutative solitons

TL;DR

This paper explores how light states on noncommutative solitons become quasi-localized, mixing with bulk modes and acquiring finite widths, especially when the world-volume gauge theory is in the Higgs phase.

Contribution

It demonstrates that in noncommutative gauge theories, light states on solitons are quasi-localized due to Higgs phase effects, with explicit examples analyzed.

Findings

Light states become quasi-localized with finite escape widths.

Widths are small compared to masses at small symmetry breaking.

Explicit examples include noncommutative vortices and instanton backgrounds.

Abstract

We consider noncommutative gauge theories which have zero mass states propagating along both commutative and noncommutative dimensions. Solitons in these theories generically carry U(m) gauge group on their world-volume. From the point of view of string theory, these solitons correspond to ``branes within branes''. We show that once the world-volume U(m) gauge theory is in the Higgs phase, light states become quasi-localized, rather than strictly localized on the soliton, i.e. they mix with light bulk modes and have finite widths to escape into the noncommutative dimensions. At small values of U(m) symmetry breaking parameters, these widths are small compared to the corresponding masses. Explicit examples considered are adjoint scalar field in the background of a noncommutative vortex in U(1)-Higgs theory, and gauge fields in instanton backgrounds in pure gauge noncommutative theories.