Dynamics of Strings in Noncommutative Gauge Theory

TL;DR

This paper presents a simple BPS soliton solution called N-fluxon in noncommutative gauge theory, analyzing its spectrum, fluctuations, and interactions, revealing insights into string-brane configurations and translational symmetries.

Contribution

The paper introduces the N-fluxon solution in noncommutative gauge theory and explores its fluctuation spectrum, interactions, and implications for translational symmetry, extending previous string-monopole work.

Findings

N-fluxon describes N D1 strings piercing a D3 brane in noncommutative space.

Spectrum includes superstring fluctuations, gauge particles, and localized states at intersections.

Translations correspond to gauge transformations plus a constant shift, affecting zero modes.

Abstract

We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point--- corresponding to fundamental strings stretched between the D1string and the D3 brane. We discuss the fluctuations about theN-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution.