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Register a new userDomain wall moduli in softly-broken SQCD at $bartheta=pi$
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We analyze the moduli space dynamics of domain walls in $SU(N)$ QCD at $bartheta=pi$, by softly breaking ${cal N}! =!1$ SQCD with sfermion mixing. In the supersymmetric limit, BPS domain walls between neighbouring vacua are known to possess non-translational flavour moduli that form a $mathcal{C} P^{N-1}$ sigma model. For the simplest case with gauge group $SU(2)$ and $N_f=2$, we show that this sigma model also exhibits a Hopf term descending from the bulk Wess-Zumino term with a quantized coefficient. On soft-breaking of supersymmetry via sfermion mixing that preserves the flavour symmetry, these walls and their moduli-space dynamics survives when $bartheta=pi$ so that there are two degenerate vacua.
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Considered are ${cal N}=2, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{rm Tr},({bar Q} Q)$ in the superpotential. ${cal N}=2$ supersymmetry is softly broken down to ${cal N}=1$ by the mass term $mu_{rm x}{rm Tr},(X^2)$ of colored adjoint scalar partners of gluons, $mu_{rm x}llLambda_2$ ($Lambda_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken flavor symmetry, $U(N_F)rightarrow U({rm n}_1)times U({rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken nontrivial $Z_{2N_c-N_Fgeq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $mgtrlessLambda_2,,, mu_{rm x}gtrless m$. The forms of low energy Lagrangians, quantum numbers of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. These calculations confirm additionally in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in recent related papers arXiv:1304.0822, arXiv:1403.6086, and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their numerous previous papers on this subject), and we explain in the text the reasons for these differences (see also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).
Considered are ${cal N}=2, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ equal mass quark flavors. ${cal N}=2$ supersymmetry is softly broken down to ${cal N}=1$ by the mass term $mu_{rm x}{rm Tr},(X^2)$ of colored adjoint scalar partners of gluons, $mu_{rm x}llLambda_2$ ($Lambda_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken global flavor symmetry, $U(N_F)rightarrow U({rm n}_1)times U({rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken non-trivial $Z_{2N_c-N_Fgeq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $mgtrlessLambda_2,,, mu_{rm x}gtrless m$. The forms of low energy Lagrangians, charges of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. The results agree with also presented in these Appendices independent calculations of these condensates using roots of the Seiberg-Witten spectral curve. This agreement confirms in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in e.g. recent related papers arXiv:1304.0822, arXiv:1403.6086 and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their previous numerous papers on this subject), and we explain in the text the reasons for these differences. (See also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).
We study the duality cascade of softly broken supersymmetric theories. We investigate the renormalization group (RG) flow of SUSY breaking terms as well as supersymmetric couplings. It is found that the magnitudes of SUSY breaking terms are suppressed in most regimes of the RG flow through the duality cascade. At one stage of cascading, the gaugino mass of the strongly coupled sector and scalar masses converge to certain values, which are determined by the gauge coupling and the gaugino mass of the weakly coupled sector. At the next stage, the strongly and weakly coupled sectors are interchanged with each other. We also show the possibility that cascading would be terminated by the gauge symmetry breaking, which is induced by the so-called B-term.
We consider supersymmetric domain walls of four-dimensional $mathcal{N}!=!1$ $Sp(N)$ SQCD with $F!=!N+1$ and $F!=!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions. When $F!=!N+2$, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue. Second, we discuss the $3d$ $mathcal{N}!=!1$ Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive $3d$ theory with the $4d$ analysis. However, for $F!=!N+2$, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our $3d$ $mathcal{N}!=!1$ gauge theories.
We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.
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