Critical Non-Abelian Vortex String and 2D N=2 Black Hole

Abstract

It has been shown that the non-Abelian vortex string in 4D $\mathcal{N}=2$ SQCD with the U(2) gauge group and $N_f=4$ flavors becomes a critical superstring. Its 10D target space is a product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was also shown that the Coulomb branch of the associated string sigma model, which opens up at strong coupling, can be described by $\mathcal{N}=2$ Liouville theory. We continue here the study of the recently proposed mass deformation of the U(2) theory with $N_f=4$, interpolating to SQCD with the U(4) gauge group and $N_f=8$ quarks, by analyzing the mass-deformed $\mathcal{N}=2$ Liouville theory on the string world sheet, and show that it is always described by the trumpet geometry of the target space, which is $T$-dual to the 2D $\mathcal{N}=2$ supersymmetric black hole. We use this correspondence to find the low-lying hadron spectrum in the deformed SQCD, and explain the expected increase in the number of hadronic states in the theory with more gauge fields and quarks by considering the near-Hagedorn behavior of the 2D black hole.