In 1979, Fradkin and Shenker observed [Phys. Rev. D 19, 3682 (1979)] that if one considers a Yang-Mills theory fully Higgsed by virtue of scalar fields in the fundamental representation of the SU(N) gauge group there is no phase transition in passing from the Higgs regime (weak coupling) to the "QCD confinement" regime at strong coupling. The above two regimes are continuously connected. We combine this observations with lessons from supersymmetric gauge theories which show that the Higgs phase is continuously connected to what is called "instead-of-confinement" phase rather than the phase with quark confinement. In the "instead-of-confinement" phase monopoles are confined and play a role of "constituent" quarks inside hadrons. In contrast, the Seiberg-Witten phase of quark confinement is not analytically connected to the Higgs phase. We propose dedicated lattice studies of Yang-Mills theories with scalar quarks.
Bibliographical noteFunding Information:
This work is supported in part by DOE grant DE-SC0011842. The work of A.Y. was supported by William I. Fine Theoretical Physics Institute of the University of Minnesota, and by Russian State Grant for Scientific Schools RSGSS-657512010.2. The work of A.Y. was supported by Russian Scientific Foundation under Grant No. 14-22-00281.
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