Related papers: 5D partition functions, q-Virasoro systems and int…

Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…

Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions…

A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor…

We study an extension of the Seiberg-Witten theory of $5d$ $\mathcal{N}=1$ supersymmetric Yang-Mills on $\mathbb{R}^4 \times S^1$. We investigate correlation functions among loop operators. These are the operators analogous to the Wilson…

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…

We provide a general formula for the partition function of three-dimensional $\mathcal{N}=2$ gauge theories placed on $S^2 \times S^1$ with a topological twist along $S^2$, which can be interpreted as an index for chiral states of the…

Chiral rings of two-dimensional (2,2) theories coupled to 4d $\mathcal{N}=2$ theories with matter hypermultiplets are studied. Specifically, the vacua of the twisted superpotential of the 2d theories with vanishing sum of matter charges are…

The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…

We examine three point functions with two scalar operators and a higher spin current in 2d W_N minimal model to the next non-trivial order in 1/N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1/N…

Let $X_1, \ldots, X_n$ be probability spaces, let $X$ be their direct product, let $\phi_1, \ldots, \phi_m: X \longrightarrow {\Bbb C}$ be random variables, each depending only on a few coordinates of a point $x=(x_1, \ldots, x_n)$, and let…

Even though matrix model partition functions do not exhaust the entire set of tau-functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial…

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over…

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…

(Chern--Simons) vector models exhibit an infinite-dimensional symmetry, the slightly-broken higher-spin symmetry with the unbroken higher-spin symmetry being the first approximation. In this note, we compute the $n$-point correlation…

Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain…

We show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of…

We derive a formula for the BPS partition functions of arbitrary S-fold theories. We first generalize the known result for the ${\cal N}=4$ $U(N)$ supersymmetric Yang-Mills theory to $SO$ and $Sp$ theories, and then we extend the formula to…

This paper explores integrable structures of a generalized melting crystal model that has two $q$-parameters $q_1,q_2$. This model, like the ordinary one with a single $q$-parameter, is formulated as a model of random plane partitions (or,…

This is a supplementary material of our recent paper\cite{yangPRB}, where a class of exactly solvable S=1 quantum Ising spin models were studied based on the hole decomposition scheme. Here we provide some details for the Green functions,…

A review on the theoretical aspects and the experimental results of polarized deep inelastic scattering and of other hard scattering processes is presented. The following items are discussed: longitudinally polarized structure functions,…