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Register a new userElliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
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We consider Seiberg electric-magnetic dualities for 4d $mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition function are described.
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Using the superconformal (SC) indices techniques, we construct Seiberg type dualities for $mathcal{N}=1$ supersymmetric field theories outside the conformal windows. These theories are physically distinguished by the presence of chiral superfields with small or negative $R$-charges.
In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.
We construct two-dimensional N=(2,2) supersymmetric gauge theories with orthogonal and symplectic groups using branes and orientifold planes in Type IIA string theory. A number of puzzles regarding the construction, including the effect of exchanging NS5-branes on an orientifold 2-plane, are resolved by lifting the configurations to M theory. The low energy properties and conjectured dualities of these theories are reproduced in the M-brane description. A similar construction of N=(4,4) theories with orthogonal and symplectic groups leads to new duality conjectures for these theories.
We study vortex solutions in a holographic model of Herzog, Hartnoll, and Horowitz, with a vanishing external magnetic field on the boundary, as is appropriate for vortices in a superfluid. We study relevant length scales related to the vortices and how the charge density inside the core of the vortex behaves as a function of temperature or chemical potential. We extract the critical superfluid velocity from the vortex solutions, study how it behaves as a function of the temperature, and compare it to earlier studies and to the Landau criterion. We also comment on the possibility of a Berezinskii-Kosterlitz-Thouless vortex confinement-deconfinement transition.
We use the superspace formulation of supergravity in eleven and ten dimensions to compute fermion couplings on the M2-brane and on D$p$-branes. In this formulation fermionic couplings arise naturally from the $theta$-expansion of the superfields from which the brane actions are constructed. The techniques we use and develop can in principle be applied to determine the fermionic couplings to general background fields up to arbitrary order. Starting with the superspace formulation of 11-dimensional supergravity, we use a geometric technique known as the `normal coordinate method to obtain the $theta$-expansion of the M2-brane action. We then present a method which allows us to translate the knowledge of fermionic couplings on the M2-brane to knowledge of such couplings on the D2-brane, and then to any D$p$-brane. This method is based on superspace generalizations of both the compactification taking 11-dimensional supergravity to type IIA supergravity and the T-duality rules connecting the type IIA and type IIB supergravities.
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