相关论文: Lens Partition Functions and Integrability Propert…

We prove a recent conjecture that the partition function of N=(2, 2) gauge theories on the two-sphere which flow to Calabi-Yau sigma models in the infrared computes the exact Kahler potential on the quantum Kahler moduli space of the…

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular…

We study 7D maximally supersymmetric Yang-Mills theory on 3-Sasakian manifolds. For manifolds whose hyper-K\"ahler cones are hypertoric we derive the perturbative part of the partition function. The answer involves a special function that…

Dispersion, impedance matching and resolution characteristics of an isotropic three-dimensional flat lens ("superlens") are studied. The lens is based on cubic meshes of interconnected transmission lines and bulk loads. We study a practical…

We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…

We study the partition functions of topologically twisted 3d $\mathcal{N}=2$ gauge theories on a hemisphere spacetime with boundary $HS^2 \times S^1$. We show that the partition function may be localised to either the Higgs branch or the…

We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…

Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…

The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the spectrum of integrable spin chains to the ground states of supersymmetric gauge theories. Up to now, this correspondence has been an observation; the underlying reason…

We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…

We consider a simple model of the dynamics of a single electron in a crystal lattice. Although this is a standard problem in condensed matter physics, alternative ways of evaluating a partition function for such a system lead to equalities,…

We calculate partition function and correlation functions in A-twisted 2d $\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the…

We study strongly correlated Hubbard systems extended to symmetric $N$-component fermions. We focus on the intermediate-temperature regime between magnetic superexchange and interaction energy, which is relevant to current ultracold…

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…

We study properties of the full partition function for the $U(1)$ 5D $\mathcal{N}=2^*$ gauge theory with adjoint hypermultiplet of mass $M$. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full…

In this succinct note, it is showed that a partition function of equivalent classes of hyperbolic surfaces can be connected to an Ising model located on the boundary of the Poincare disc, as hinted by Poincare's Uniformization theorem and…

Partition functions for M2-brane theories in various backgrounds are computed. We consider in particular configurations of membranes at orbifold singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane theory for some of…

The quasi-classical expansion of a multicomponent spin solution of the star-star relation with hyperbolic Boltzmann weights is investigated. The equations obtained in a quasi-classical limit provide n-1-component extensions of certain…