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## NS three-form flux deformation for the critical non-Abelian vortex string

It has been shown that the non-Abelian solitonic 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 low-lying closed string states in the associated type-IIA string theory was found and interpreted

as a spectrum of hadrons in 4D N = 2 SQCD. In particular, the lowest string state appears to be a massless

BPS baryon associated with the deformation of the complex structure modulus b of the conifold. In the

previous work the deformation of the ten-dimensional background with nonzero Neveu-Schwarz 3-form

flux was considered and interpreted as a switching on a particular choice of quark masses in 4D SQCD.

This deformation was studied to leading order at small 3-form flux. In this paper we study the back reaction

of the nonzero 3-form flux on the metric and the dilaton introducing the ansatz with several warp factors

and solving the gravity equations of motion.We show that 3-form flux produces a potential for the conifold

complex structure modulus b, which leads to the runaway vacuum. At the runaway vacuum warp factors

disappear, while the conifold degenerates. In 4D SQCD we relate this to the flow to the U(1) gauge theory

upon switching on quark masses and decoupling of two flavors.