Related papers: On theta function expressions of cyclic products o…

Results for $\beta$-functions and anomalous dimensions in general scalar fermion theories are presented to three loops. Various constraints on the individual coefficients for each diagram following from supersymmetry are analysed. The…

In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary…

We analyze the divergent part of the one-loop effective action for the noncommutative SU(2) gauge theory coupled to the fermions in the fundamental representation. We show that the divergencies in the 2-point and the 3-point functions in…

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with…

There are few constructions of square-integrable automorphic functions on metaplectic groups. Such functions may be obtained by the residues of certain Eisenstein series on covers of groups, "theta functions," but the Fourier coefficients…

In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting shape of the crank generating function. We fit this function in a more general family of inverse theta functions which play a key role in physics.

The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces. Our definition of the odd higher genus sigma-function is based on a generalization of the classical representation…

We study complex zeros of the partition function of 2-spin systems, viewed as a multivariate polynomial in terms of the edge interaction parameters and the uniform external field. We obtain new zero-free regions in which all these…

We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way…

We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal…

The slice-independent gauge-fixed superstring chiral measure in genus 2 derived in the earlier papers of this series for each spin structure is evaluated explicitly in terms of theta-constants. The slice-independence allows an arbitrary…

Ferroelectric GeTe is unveiled to exhibit an intriguing multiple non-trivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting…

The string theory on symmetric product describes the second-quantized string theory. The development for the bosonic open string was discussed in the previous work. In this paper, we consider the open superstring theory on the symmetric…

We show that one-parameter deformation $\mathcal A_{q,t}$ of the skein algebra $Sk_q(\Sigma_2)$ of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we…

In this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves $X_s$ defined by the equation $y^3 =x(x-s)(x-b_1)(x-b_2)$ in the affine $(x,y)$ plane, for $s\in D_\varepsilon:=\{s \in \mathbb{C} |…

We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong coupling problem, with no small parameter other than…

We define and compute the continuous orbifold partition function and a generating function for all $n$-point correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface formed by…

Nucleon structure functions are shown to have a qualitative (or `formal') relation to the classical elliptic theta functions. In particular, theta_1'/2 shows a clear resemblance to a non-singlet structure function like xF_3. In the…

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing $F$-matrices (or the so-called $F$-basis) play an important…

We compute the single-interval Renyi entropy (replica partition function) for free fermions in 1+1d at finite temperature and finite spatial size by two methods: (i) using the higher-genus partition function on the replica Riemann surface,…