Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String

TL;DR

This paper investigates how NS 3-form flux influences the vacua of a critical non-Abelian vortex string, deriving the potential for the conifold's complex structure modulus and analyzing the back reaction, revealing a runaway vacuum with conifold degeneration.

Contribution

It provides an exact potential for the conifold modulus induced by NS 3-form flux and includes back reaction effects, advancing understanding of flux-induced vacua in string-like solitons.

Findings

Derived the exact potential for the conifold modulus from 3-form flux.

Solved gravity equations including back reaction effects.

Found a runaway vacuum leading to conifold degeneration.

Abstract

It has been demonstrated that the non-Abelian solitonic vortex string in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group U(2) and $N_f=4$ quark hypermultiplets behaves as a critical superstring. This string propagates in a ten-dimensional space comprising the flat 4D space and an internal Calabi-Yau noncompact threefold, specifically, the conifold. The lowest state of this string is a massless BPS baryon associated with the deformation of the conifold's complex structure modulus, $b$. Previous studies considered deformations of the 10-dimensional background by a nonzero Neveu-Schwarz (NS) 3-form flux, which was interpreted as selecting specific quark masses in 4D SQCD. These deformations and the corresponding back reaction on the metric were analyzed at the leading order at small 3-form flux. In this paper, we first derive the exact potential for the conifold complex structure modulus $b$ generated by the 3-form flux assuming a fixed conifold background. Then we include the back reaction effects and solve the corresponding gravity equations of motion. We show that the resulting potential gives a runaway vacuum. At this runaway vacuum the conifold undergoes degeneration.