Critical non-Abelian vortex string and 2D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> black hole

It has been shown that the non-Abelian vortex string in 4D <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">N</a:mi> <a:mo>=</a:mo> <a:mn>2</a:mn> </a:math> supersymmetric QCD (SQCD) with the U(2) gauge group and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>N</d:mi> <d:mi>f</d:mi> </d:msub> <d:mo>=</d:mo> <d:mn>4</d:mn> </d:math> 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi mathvariant="script">N</f:mi> <f:mo>=</f:mo> <f:mn>2</f:mn> </f:math> Liouville theory. We continue here the study of the recently proposed mass deformation of the U(2) theory with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>N</i:mi> <i:mi>f</i:mi> </i:msub> <i:mo>=</i:mo> <i:mn>4</i:mn> </i:math> , interpolating to SQCD with the U(4) gauge group and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>N</k:mi> <k:mi>f</k:mi> </k:msub> <k:mo>=</k:mo> <k:mn>8</k:mn> </k:math> quarks, by analyzing the mass-deformed <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi mathvariant="script">N</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:math> Liouville theory on the string world sheet, and show that it is always described by the trumpet geometry of the target space, which is <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>T</p:mi> </p:math> -dual to the 2D <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi mathvariant="script">N</r:mi> <r:mo>=</r:mo> <r:mn>2</r:mn> </r:math> 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.