Mass spectra in ${\cal N}=1$ SQCD with additional colorless fields and problems with Seiberg's duality
Victor L. Chernyak
备注：
16 pages. Small improvements in the text, one reference added, results unchanged. Talk given at Session of Nucl.Phys. section of RAS, Novosibirsk, Russia, 10-12 March 2020. arXiv admin note: text overlap with arXiv:1906.08643
Considered is the direct ${\cal N}=1$ SQCD-like $Φ$-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 $Φ_{i}^{j}$ with the large mass parameter $μ_Φ\ggΛ_Q$, interacting with quarks through the Yukawa coupling. In parallel, is considered its Seiberg's dual variant, i.e. the $dΦ$-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 $μ<Λ_Q$. 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 $Φ$ `return back' and there appear two additional generations of light $Φ$-particles with small masses $μ^{\rm pole}_{2,3}(Φ)\llΛ_Q$.
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.
Mass Spectra in ${\cal N}=1$ SQCD, in ${\cal N}=1$ SQCD-type theory and in softly broken ${\cal N}=2\rightarrow {\cal N}=1$ SQCD. And problems with the ${\cal N}=1$ Seiberg duality
This paper continues our previous study of similar theories in \cite{ch5}. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual with $SU(N_F-N_c)$ dual colors) and $N_F$ flavors of light quarks, and with $N_F^2$ additional colorless flavored fields $Φ^j_i$, but now with $N_F$ in the range $2N_c<N_F<3N_c$. The multiplicities of various vacua and quark and gluino condensates in these vacua are found. The mass spectra of the direct and Seiberg's dual theories in various vacua are calculated within the dynamical scenario which assumes that quark…
This paper continues our studies in arXiV:1608.06452 [hep-th] of ${\cal N}=1$ gauge theories in the strongly coupled regimes. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual), with $N_F$ flavors of light quarks and $N_F^2$ additional colorless flavored scalars $Φ^j_i$, but now with $N_F$ in the range $N_F>3N_c$. The mass spectra of these direct and dual theories in various vacua are calculated within the dynamical scenario introduced by the author in [8]. It assumes that quarks in such ${\cal N}=1$ SQCD-like theories without elementary …
Considered is the ${\cal N}=1$ SQCD-like theory with $SU(N_c)$ colors and $0< N_F<2N_c$ flavors of equal mass $0< m_Q\llΛ_Q$ quarks. Besides, it includes $N^2_F$ additional colorless but flavored fields $Φ_{i}^{j}$, with the large mass parameter $μ_Φ\ggΛ_Q$. The mass spectra of this $Φ$-theory are first directly calculated at $0<N_F<N_c$ where the quarks are weakly coupled, in all different vacua with the unbroken or spontaneously broken flavor symmetry $U(N_F)\rightarrow U(n_1)\times U(n_2)$. Further, the mass spectra of this direct $Φ$-theory and its Seiberg's dual variant, the $dΦ$-theory, …
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Twisted supersymmetric theories on a product of two Riemann surfaces possess non-local holomorphic currents in a BRST cohomology. The holomorphic currents act as vector fields on the chiral ring. The OPE's of these currents are invariant under the renormalization group flow up to BRST-exact terms. In the context of electric-magnetic duality, the algebra generated by the holomorphic currents in the electric theory is isomorphic to the one on the magnetic side. For the currents corresponding to global symmetries this isomorphism follows from 't Hooft anomaly matching conditions. The isomorphism …
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We present a new duality between the F-terms of supersymmetric field theories defined in two- and four-dimensions respectively. The duality relates N=2 supersymmetric gauge theories in four dimensions, deformed by an Omega-background in one plane, to N=(2,2) gauged linear sigma-models in two dimensions. On the four dimensional side, our main example is N=2 SQCD with gauge group SU(L) and 2L fundamental flavours. Using ideas of Nekrasov and Shatashvili, we argue that the Coulomb branch of this theory provides a quantization of the classical Heisenberg SL(2) spin chain. Agreement with the standa…
