Twisted-Mass Potential on the Non-Abelian String World Sheet Induced by Bulk Masses

TL;DR

This paper provides a direct derivation of the twisted-mass potential on the non-Abelian string world sheet from the bulk N=2 theory with massive quarks, confirming previous indirect results and analyzing the effects of bulk mass terms.

Contribution

It presents the first direct derivation of the twisted-mass potential from the bulk theory and computes the resulting $| |$ potential in the effective world sheet theory.

Findings

Confirmed the form of the $| |$ potential due to bulk mass terms

Derived the profile functions of adjoint fields explicitly

Validated the effective theory predictions with direct bulk analysis

Abstract

We derive the twisted-mass potential in N=(2,2) CP(N-1) theory on the world sheet of the non-Abelian string from the bulk N=2 theory with massive (s)quarks by determining the profile functions of the adjoint fields. Although this potential was indirectly found some time ago, this is the first direct derivation from the bulk. As an application of the adjoint field profiles, we compute and confirm the $ | \mu \sigma | $ potential (where $ \sigma $ is a scalar field in the gauge supermultiplet) which arises in the effective two-dimensional theory on the string due to the supersymmetry breaking bulk mass term $ \mu A^2 $ for the adjoint matter.