Critical non-Abelian vortex string and 2D N = 2 black hole

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2025. Vol. 112. No. 10. Article 105010.

Evgenii Ievlev, Andrei Marshakov, Sumbatian G., Alexei Yung

It has been shown that the non-Abelian vortex string in 4D N = 2 supersymmetric QCD (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 N = 2 Liouville theory. We continue here the study of the recently
proposed mass deformation of the U(2) theory with Nf ¼ 4, interpolating to SQCD with the U(4) gauge
group and N_f =8 quarks, by analyzing the mass-deformed 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 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.

Keywords: string theory, gauge theories, supersymmetry, Sigma Models, vortices