Fractional Strings in (p,q) 5-brane and Quiver Matrix String Theory

TL;DR

This paper explores the dynamics of fractional strings in (p,q) 5-branes using Matrix string theory, revealing their moduli space, behaviors, and the transition processes between different branches, with implications for gauge theory monodromies.

Contribution

It introduces a new Matrix string theory description of fractional strings and analyzes their moduli space and transition mechanisms in (p,q) 5-brane systems.

Findings

Fractional strings appear as instantons in 5-brane gauge theory.

The moduli space metrics of fractional strings are calculated.

Joining of fractional strings corresponds to Coulomb-Higgs branch transition.

Abstract

We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theory in the T-dualized ALE background. The most remarkable feature in the (p,q)5-brane is the existence of ``fractional string'', which appears as the instanton of 5-brane gauge theory. We approach to the physical aspects of fractional string by means of the two types of Matrix string probes: One of which is that given in hep-th/9710065. As the second probe we present the Matrix string theory describing the fractional string itself. We calculate the moduli space metrics in the respective cases and argue on the specific behaviors of fractional string. Especially, we show that the ``joining'' process of fractional strings can be realized as the transition from the Coulomb branch to the Higgs branch of the fractional string probe. In this argument, we emphasize the importance of some monodromies related with the theta-angle of the 5-brane gauge theory.