Unstable Solitons in Noncommutative Gauge Theory

TL;DR

This paper discovers exact unstable soliton solutions in noncommutative gauge theories, linking them to non-supersymmetric D-brane configurations and analyzing their fluctuation spectra, including tachyon condensation.

Contribution

It introduces new unstable non-BPS soliton solutions in noncommutative gauge theories and relates them to D-brane configurations in string theory.

Findings

Localized solutions with magnetic flux in 2D noncommutative U(1) theory

Non-BPS solutions with the same Pontrjagin charge but higher energy than instantons in 4D

Spectrum analysis showing tachyon and endpoint of condensation as dissolved branes

Abstract

We find a class of exact solutions of noncommutative gauge theories corresponding to unstable non-BPS solitons. In the two-dimensional euclidean (or 2+1 dimensional lorentzian) U(1) theory we find localized solutions carrying nonzero magnetic flux. In four euclidean dimensions we find non-BPS solutions with the same Pontrjagin charge but greater energy than the usual self-dual Yang-Mills instanton. We conjecture that these solutions and generalizations thereof correspond to nonsupersymmetric configurations of D-(p-2k) branes (or intersections thereof) in a D-p brane in the noncommutative scaling limit of large B-field. In the particular case of a 0-brane on a 2-brane the analysis of small fluctuations reveals an infinite tower of states which agrees exactly with that of the 0-2 CFT in the scaling limit. The spectrum contains a tachyon, and we show explicitly that the endpoint of tachyon condensation corresponds to the 0-brane dissolved in the 2-brane.