Related papers: The regularization of Dotsenko--Fateev integrals
We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ's minimal models of 2D CFT as described by Felder and Silvotti and Dotsenko and…
We point out that there is a generalization to higher dimensions $d=2h>2$ of the two-dimensional Dotsenko-Fateev formula \DF\ for particular Coulomb gas conformal invariant integrals. These expressions represent structure constants of…
We develop a method for evaluating asymptotics of certain contour integrals that appear in Conformal Field Theory under the name of Dotsenko-Fateev integrals and which are natural generalizations of the classical hypergeometric functions.…
The second-order partial derivatives of the Coulomb potential of a point charge can be regularized using the Coulomb potential of a charge of the oblate spheroidal shape that a moving rest-frame-spherical charge acquires by the Lorentz…
We give a brief account of the key properties of elliptic hypergeometric integrals -- a relatively recently discovered top class of transcendental special functions of hypergeometric type. In particular, we describe an elliptic…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
The purpose of this article is to present a new regularization technique of quasi-plurisubharmoinc functions on a compact Kaehler manifold. The idea is to regularize the function on local coordinate balls first, and then glue each piece…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the…
The perturbative construction of the S-matrix in the causal spacetime approach of Epstein and Glaser may be interpreted as a method of regularization for divergent Feynman diagrams. The results of any method of regularization must be…
We give a brief review of the main results of the theory of elliptic hypergeometric functions -- a new class of special functions of mathematical physics. We prove the most general univariate exact integration formula generalizing Euler's…
It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use…
Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a…
We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show…
We consider Rota-Baxter algebras of meromorphic forms with poles along a (singular) hypersurface in a smooth projective variety and the associated Birkhoff factorization for algebra homomorphisms from a commutative Hopf algebra. In the case…
Moreau-Yosida regularization is introduced into the framework of exact DFT. Moreau-Yosida regularization is a lossless operation on lower semicontinuous proper convex functions over separable Hilbert spaces, and when applied to the…
This paper is devoted to study the generic fold-fold singularity of Filippov systems on the plane, its unfoldings and its Sotomayor-Teixeira regularization. We work with general Filippov systems and provide the bifurcation diagrams of the…
The holomorphic Coulomb gas formalism is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of QFT. We begin with a careful examination…