Mass Spectra in $$\boldsymbol{\mathcal{N}=1SQCD}$$ with Additional Colorless Fields and Problems with the Seiberg Duality

Abstract

Considered is the direct ${\cal N}=1$ SQCD-like $\Phi$-theory with $SU(N_c)$ colors and $3N_c/2< N_F<2N_c$ flavors of light quarks ${\overline Q},\,Q$. Besides, it includes $N^2_F$ additional colorless but flavored fields $\Phi_{i}^{j}$ with the large mass parameter $\mu_{\Phi}\gg\Lambda_Q$, interacting with quarks through the Yukawa coupling. In parallel, is considered its Seiberg's dual variant, i.e. the $d\Phi$-theory with $(N_F-N_c)$ dual colors, $N_F$ flavors of dual quarks ${\overline q},\,{q}$ and $N_F^2$ elementary mion fields $M^i_j\rightarrow ({\overline Q}_j Q^i)$. In considered here vacua, the quarks of both theories are in the conformal regimes at scales $\mu<\Lambda_Q$. The mass spectra are calculated in sections 4 and 5. It is shown that they are different in the direct and dual theories, in disagreement with the Seiberg hypothesis about equivalence of two such theories. Besides it is shown in the direct theory that a qualitatively new phenomenon takes place: the seemingly heavy fields $\Phi$ `return back' and there appear two additional generations of light $\Phi$-particles with small masses $\mu^{\rm pole}_{2,3}(\Phi)\ll\Lambda_Q$. In Conclusions also presented comparison of mass spectra of these two theories for such values of parameters when the direct theory is in the very strong coupling regime, while the dual one is in the weak coupling IR-free logarithmic regime. It is shown that mass spectra of these two theories are parametrically different in this case.