Critical non-Abelian vortices and holography for little string theory

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2021. Vol. 104. No. 11. Article 114033.

E. Ievlev, A. Yung

It has been shown that non-Abelian vortex string supported in four-dimensional (4D) N =2
supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of
closed string states of the associated string theory was obtained using the equivalence between the critical
string on the conifold and the noncritical string on the semi-infinite cigar described by the SL(2;R)/U(1) Wess-Zumino-Novikov-Witten model. This spectrum was identified with the spectrum of hadrons in 4D
N = 2 SQCD. In order to describe effective interactions of these 4D hadrons in this paper, we study
correlation functions of normalizable vertex operators localized near the tip of the SL(2,R)/U(1) cigar.We
also compare our solitonic string approach to the gauge-string duality to the AdS/CFT-type holography for
little string theories. The latter relates off mass-shell correlation functions on the field theory side to
correlation functions of non-normalizable vertex operators on the cigar. We show that in most channels the
holographic approach works in our theory because normalizable and non-normalizable vertex operators
with the same conformal dimension are related due to the reflection from the tip of the cigar. However, we
find that holography does not work for lightest hadrons with given baryonic charge.

Keywords: quantum field theory, string theory, Supersymmetry