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.

43 pages, 3 figures, v4: published version

References in corpus (25)

• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Liouville Field Theory -- A decade after the revolution
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• A Matrix Model for the Two Dimensional Black Hole
• Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• Quantum Vortex Strings: A Review
• LSZ in LST
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• Perturbative String Thermodynamics near Black Hole Horizons
• Critical String from Non-Abelian Vortex in Four Dimensions
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
• Lessons from supersymmetry: "Instead-of-Confinement" Mechanism
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory
• String "Baryon'' in Four-Dimensional $\mathcal{N}=2$ Supersymmetric QCD from 2D-4D Correspondence
• Critical Non-Abelian Vortex and Holography for Little String Theory
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory