Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality

TL;DR

This paper explores the transition between weak and strong coupling regimes in N=2 supersymmetric U(N) gauge theories, revealing a dual weakly coupled theory with a different gauge group and analyzing non-Abelian strings and their excitations.

Contribution

It demonstrates the existence of a dual weakly coupled N=2 theory at strong coupling with a different gauge group and analyzes the behavior of non-Abelian strings across the transition.

Findings

Dual weakly coupled N=2 theory with gauge group U(N_f-N) at strong coupling.

Interchange of elementary and composite excitations across the transition.

Possible relation of composite stringy states to Seiberg's M fields.

Abstract

The crossover transition from weak coupling at large \xi to strong coupling at small \xi is studied in N=2 supersymmetric gauge theory with the U(N) gauge group and N_f>N (here \xi is the Fayet--Iliopoulos parameter). We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small \xi. The dual gauge group is U(N_f-N). The dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both theories support non-Abelian strings. In each of these two regimes there are two varieties of physical excitations: elementary fields and nonperturbative composite states bound by confining strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields.