相关论文: Mordell integrals and Giveon-Kutasov duality

We show that interval partition functions (transition amplitudes) of three-dimensional $N = 2$ theories admit factorizations into sums of products of hemisphere partition functions with additional normalization factors. We prove the…

The N = 1 supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken N = 2 rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the…

We consider the Sine-Gordon model coupled to 2D gravity. We find a nonperturbative expression for the partition function as a function of the cosmological constant, the SG mass and the SG coupling constant. At genus zero, the partition…

We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on…

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along…

We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…

We study the partition function of the N=6 supersymmetric U(N_1)_k x U(N_2)_{-k} Chern-Simons-matter (CSM) theory, also known as the ABJ theory. For this purpose, we first compute the partition function of the U(N_1) x U(N_2) lens space…

We study supersymmetric Yang-Mills theories on the three-sphere, with massive matter and Fayet-Iliopoulos parameter, showing second order phase transitions for the non-Abelian theory, extending a previous result for the Abelian theory. We…

We compute exactly the partition function of two dimensional N=(2,2) gauge theories on S^2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and anti-vortex excitations on…

We derive the partition function of {\cal N}=4 supersymmetric Yang-Mills theory on orbifold-T^4/{\bf Z}_2 for gauge group SU(N). We generalize the method of our previous work for the SU(2) case to the SU(N) case. The resulting partition…

Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…

We study matrix integration over the classical Lie groups $U(N),Sp(2N),O(2N)$ and $O(2N+1)$, using symmetric function theory and the equivalent formulation in terms of determinants and minors of Toeplitz$\pm$Hankel matrices. We establish a…

In this thesis we will study matrix models with discrete gauge group $S_N$. We will put these matrix models into a generalized Schur-Weyl duality framework where dual algebras, known as partition algebras, emerge. These form generalizations…

U(1) gauge theory on ${\bf R}^4$ is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of $SL(2,{\bf Z})$. In this paper, the duality is studied on a general four-manifold and…

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form $ _{0}{\mathcal{D}}_{t}^{2\tau}u^{} + \sum_{i=1}^{d}$ $[c_{l_i}$…

We study $U(N)_k$ Chern-Simons theory coupled to fundamental fermions and scalars in a large $N$ `t Hooft limit. We compute the thermal free energy at high temperature, as well as two- and three-point functions of simple gauge-invariant…

We construct the Fermi gas formalism for the partition function of supersymmetric Chern-Simons theories with affine $D$-type quiver diagrams with non-uniform ranks of the gauge groups and Fayet-Illiopoulos parameters by two different…

In this work, we revisit the exact computation of the round sphere partition function of 3d $\mathcal{N}=4$ circular quiver Chern-Simons theories with mass and Fayet-Iliopoulos (FI) deformations. Utilizing the Fermi gas formalism, we derive…

By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The…

In [arXiv:1805.05057 [hep-th]],[arXiv:1812.00811 [hep-th]], the partition function of the Gross-Witten-Wadia unitary matrix model with the logarithmic term has been identified with the $\tau$ function of a certain Painlev\'{e} system, and…