Flux compactification for the critical non-Abelian vortex and quark masses

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2021. Vol. 104. No. 2. Article 025007.

A. Yung

It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D)
N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f =4 quark flavors behave
as critical superstrings. In addition to four translational moduli, the non-Abelian strings under
consideration carry six orientational and size moduli. Together they form a ten-dimensional space
required for a superstring to be critical. The target space of the string sigma model is a product of the
flat four-dimensional space R4 and a Calabi-Yau noncompact threefold Y_6, 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 Bogomolny-Prasad-Sommerfeld baryon associated with the deformation of the complex
structure modulus b of the conifold. Here we address a problem of switching on quark masses in 4D
SQCD, which classically breaks the world sheet conformal invariance in the string sigma model. To
avoid this problem we follow a standard string theory approach and use a flux “compactification” to lift
the complex structure modulus of the conifold. Namely, we find a solution of supergravity equations of
motion with nonzero Neveu-Schwarz 3-form flux. It produces a potential for the baryon b, which leads
to the runaway vacuum. Using field theory arguments, we interpret 3-form flux in terms of a particular
choice of quark masses in 4D SQCD. At the runaway vacuum the conifold degenerates to lower
dimensions. We interpret this as a flow from a non-Abelian string to an Abelian one.

Keywords: string theory, Supersymmetry, gauge theories, monopoles