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Register a new userNew Examples of Duality in Chiral and Non-Chiral Supersymmetric Gauge Theories
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We present evidence for renormalization group fixed points with dual magnetic descriptions in fourteen new classes of four-dimensional $N=1$ supersymmetric models. Nine of these classes are chiral and many involve two or three gauge groups. These theories are generalizations of models presented earlier by Seiberg, by Kutasov and Schwimmer, and by the present authors. The different classes are interrelated; one can flow from one class to another using confinement or symmetry breaking.
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We study $N=1$ SUSY gauge theories in four dimensions with gauge group $Spin(7)$ and $N_f$ flavors of quarks in the spinorial representation. We find that in the range $6< N_f < 15$, this theory has a long distance description in terms of an $SU(N_f-4)$ gauge theory with a symmetric tensor and $N_f$ antifundamentals. As a spin-off, we obtain by deforming along a flat direction a dual description of the theories based on the exceptional gauge group $G_2$ with $N_f$ fundamental flavors of quarks.
We compare gap equation predictions for the spontaneous breaking of global symmetries in supersymmetric Yang-Mills theory to nonperturbative results from holomorphic effective action techniques. In the theory without matter fields, both approaches describe the formation of a gluino condensate. With $N_f$ flavors of quark and squark fields, and with $N_f$ below a certain critical value, the coupled gap equations have a solution for quark and gluino condensate formation, corresponding to breaking of global symmetries and of supersymmetry. This appears to disagree with the newer nonperturbative techniques, but the reliability of gap equations in this context and whether the solution represents the ground state remain unclear.
We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.
It has been conjectured that duality cascade occurs in the $mathcal{N}=3$ supersymmetric Yang-Mills Chern-Simons theory with the gauge group $U(N )_k times U(N+M )_{-k}$ coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $mathcal{N}=3$ supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on $S^3$ partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.
We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the index. In our investigations we also clarify several related issues.
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