Quark Number Fractionalization in N=2 Supersymmetric $SU(2) \times U(1)^{N_f}$ Gauge Theories

TL;DR

This paper calculates quark-number charges of dyons in N=2 supersymmetric gauge theories, revealing that massless monopoles have zero quark number and resolving related CP invariance issues, with results extendable to larger gauge groups.

Contribution

It generalizes Witten's electric charge formula to quark numbers in N=2 supersymmetric theories with SU(2)×U(1)^{N_f} gauge group, providing new insights into dyon charges.

Findings

Quark numbers of massless monopoles vanish at nondegenerate singularities.

A CP invariance related puzzle is resolved.

Results are extendable to SU(N_c)×U(1)^{N_f} gauge theories.

Abstract

Physical quark-number charges of dyons are determined, via a formula which generalizes that of Witten for the electric charge, in N=2 supersymmetric theories with $SU(2) \times U(1)^{N_f} $ gauge group. The quark numbers of the massless monopole at a nondegenerate singularity of QMS turn out to vanish in all cases. A puzzle related to CP invariant cases is solved. Generalization of our results to $SU(N_c)\times U(1)^{N_f}$ gauge theories is straightforward.