String "Baryon'' in Four-Dimensional $\mathcal{N} = 2$ Supersymmetric QCD from 2D-4D Correspondence

TL;DR

This paper demonstrates the existence of a massless BPS baryon in 4D $ ext{N}=2$ supersymmetric QCD by analyzing non-Abelian vortex strings and their associated 2D world-sheet theories, revealing a deep 2D-4D correspondence.

Contribution

It provides a field-theoretic derivation of a stringy baryon in 4D $ ext{N}=2$ SQCD using the weighted $ ext{CP}$ model and mirror symmetry, connecting string theory results with gauge theory.

Findings

Identification of a massless BPS baryon in 4D SQCD.

Connection between conifold deformation and Higgs branch emergence.

Validation of string theory predictions through field-theoretic methods.

Abstract

We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string -- the so called weighted $\mathcal{N} = (2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional non-compact Calabi-Yau space $Y_6$, the conifold. We use mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a non-perturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS "baryon" previously found in string theory.