Related papers: On affine coordinates of the tau-function for open…
This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square…
In this paper we obtain large $z$ asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlev\'e II differential equation. Using the fact that these tau functions can be written…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…
In this paper we briefly review the main idea of the localization technique and its extension suitable in supersymmetric gauge field theory. We analyze the partition function of the vector multiplets with supercharges and its blocks on the…
We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general $G_f$ is a central extension of the bosonic symmetry group $G_b$ by…
We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Petviashvili tau functions of hypergeometric type (also known…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the…
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations appears as a specific subset of the $n$-component KP…
The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract Interpolation Problem is formulated which seems…
It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
In 2003, Ozsv\'ath and Szab\'o defined the concordance invariant $\tau$ for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of $\tau$ for knots in $S^3$ and a…
These lectures were prepared to be presented at A.A. Belavin seminar on CFT at Landau Institute for Theoretical Physics. We review bosonization of CFT and show how it can be applied to the studying of representations of…
Asymptotic expansions for the Bateman and Havelock functions defined respectively by the integrals \[\frac{2}{\pi}\int_0^{\pi/2} \!\!\!\begin{array}{c} \cos\\\sin\end{array}\!(x\tan u-\nu u)\,du\] are obtained for large real $x$ and large…
Conventional estimators of the anisotropic power spectrum and two-point correlation function (2PCF) adopt the `Yamamoto approximation', fixing the line-of-sight of a pair of galaxies to that of just one of its members. Whilst this is…
This paper provides a short introduction to scalar, bosonic, and fermionic superfield component expansion based on the branching rules of irreducible representations in one Lie algebra (in our case, $\mathfrak{su}(32)$, and also…
We describe the points of diff erentiability of the multiplicative autocorrelation function of the "fractional part" function. In connection with this question, we study series involving the fi rst Bernoulli function, the arithmetical…
The aim of the paper is to formulate a discrete analogue of the claim made by Alvarez-Gaume et al., realizing the partition function of the free fermion on a closed Riemann surface of genus g as a linear combination of 2^{2g} Pfaffians of…