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Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a…
A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kaehler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the…
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative…
The supersymmetric cigar (half-)index or cigar partition function of 3d $\mathcal{N}=2$ gauge theories contains a wealth of information. Physically, it captures the spectrum of BPS states, the non-perturbative corrections to various…
The partition function (quantum transition amplitude) of the gauge system with gauge group $Z_2$ coupled with Majorana fermions is calculated on the regular 3D cubic lattice.
This is the 9th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. We review the exact computations in 3D N=2 supersymmetric gauge theories on the round or squashed $S^3$ and the…
We consider the 4d superconformal index for ${\cal N}=2$ gauge theories on $S^1 \times L(r,1)$, where $L(r,1)$ is a Lens space. We focus on a one-parameter slice of the three-dimensional fugacity space and in that sector we show S-duality.…
We study three-dimensional supersymmetric quiver gauge theories with a non-simply laced global symmetry primarily focusing on framed affine $B_{N}$ quiver theories. Using a supersymmetric partition function on a three sphere, and its…
We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7,1) and L(7,2). The invariants are built on the base of a classical (not quantum) solution of…
Recently I proposed a new calculation scheme of a partition function of an immersion object using path integral method and theory of soliton (to appear in J.Phys.A). I applied the scheme to problem of elastica in two-dimensional space and…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In this brief review, we discuss a program of constructing…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
The relation between the 2d Ising partition function and spin network evaluations, reflecting a bulk-boundary duality between the 2d Ising model and 3d quantum gravity, promises an exchange of results and methods between statistical physics…
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…
We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry localization, we show that the $T^2 \times S^2$ partition function is given by elliptic genus of…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold $M$ with complex gauge group $G$. We focus on the case $G=SL(N,\mathbb{C})$ and with $M$ a knot complement. The main result presented in this note is the…
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric…
We evaluate the superconformal index of 4d $\mathcal{N}=4$ SYM with gauge algebra $so(2N_c+1)$ in the Cardy-like limit. We then study the relation with the results obtained for the S-dual $usp(2N_c)$, discussing the fate of S-duality in…