String baryon in four-dimensional N=2 supersymmetric QCD from the 2D-4D correspondence

Physical Review D - Particles, Fields, Gravitation and Cosmology. 2020. Vol. 102. No. 5. Article 054026.

E. Ievlev, Shifman M., A. Yung

We study non-Abelian vortex strings in four-dimensional (4D) N = 2 supersymmetric QCD with the
U(2) gauge group and N_f =4 flavors of quark hypermultiplets. It has recently been shown that these
vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory
was found and interpreted as a spectrum of hadrons in 4D N = 2 supersymmetric QCD. In particular, the
lowest string state appears to be a massless Bogomol’nyi-Prasad-Sommerfield (BPS) “baryon.” Here we
show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the
conformal world-sheet theory on the non-Abelian string—the so-called weighted N =(2; 2) supersymmetric
CP model. Its target space is given by the six-dimensional noncompact Calabi-Yau space Y_6, the
conifold.We use a mirror description of the model to study the BPS kink spectrum and its transformations on
curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of
the complex structure of the conifold is associated with the emergence of a nonperturbative Higgs branch in
4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum
expectation value of the massless BPS baryon previously found in string theory.

Keywords: quantum field theory, gauge theories, supersymmetry