The Holomorphic Tension of Nonabelian Vortices

TL;DR

This paper calculates the BPS tension of nonabelian vortices in supersymmetric gauge theories with degenerate masses, revealing a simple relation in the chiral ring and proposing a duality interpretation.

Contribution

It extends previous work by considering degenerate masses and computes the vortex tension in the strong coupling regime, proposing a conjecture for its validity beyond that regime.

Findings

BPS tension equals a simple chiral ring quantity

Conjecture of tension validity outside strong coupling

Evidence for a duality r <--> N_f - r

Abstract

We continue the work hep-th/0411075 considering here the case of degenerate masses. A nonabelian vortex arises in r-vacua upon the breaking by a superpotential for the adjoint field. We find the BPS tension in the strong coupling regime computing the dual-quark condensate. Then we find that it is equal to a simple quantity in the chiral ring of the theory and so we conjecture the validity of our result out of the strong coupling regime. Our result gives an interesting hint about the duality r <--> N_f-r, seeing it as the exchange first <--> second sheet of N=1 Riemann surface.