Related papers: Theta function parameterization and fusion for 3-D…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
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…
Theta functions play a major role in many current researches and are powerful tools for studying integrable systems. The purpose of this paper is to provide a short and quick exposition of some aspects of meromorphic theta functions for…
Covariant density functional theory is solved in 3D lattice space by implementing the preconditioned conjugate gradient method with a filtering function (PCG-F). It considerably improves the computational efficiency compared to the previous…
Yang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. Finding the solutions of these equations is a formidable task. In this work we develop a systematic…
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…
We obtain a new solution of the star-triangle relation with positive Boltzmann weights which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines…
The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…
Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the…
We discuss a class of solutions to the Ernst equation in terms of theta functions with characteristics. We show that it is necessary to take into account a phase factor, which arises from a shift by a lattice vector, and impose conditions…
We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a…
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…
The $A^{(1)}_{n-1}$-face model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We construct the fused boundary Boltzmann weights to determine the normalization factor. We derive difference equations of the…
We define a regularized Shintani theta lift which maps weight $2k+2$ ($k \in \Z, k \geq 0$) harmonic Maass forms for congruence subgroups to (sesqui-)harmonic Maass forms of weight $3/2+k$ for the Weil representation of an even lattice of…
We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the…
We find the fermionic R-operator based on Bazhanov-Stroganov three-parameter elliptic parametrization of the free fermion model, and the corresponding Yang-Baxter and decorated Yang-Baxter equations, which are of the difference type in one…
We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these…
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…
We give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two classes of lattice models: the classical…