Related papers: Two dialects for KZB equations: generating one-loo…
It was known through the efforts of many works that the generating functions in the closed Gromov-Witten theory of $K_{\mathbb P^2}$ are meromorphic quasi-modular forms basing on the B-model predictions. In this article, we extend the…
We reexamine genus one super-Green functions with general boundary conditions twisted by $(\alpha, \beta)$ for $(\sigma, \tau)$ directions in the eigenmode expansion and derive expressions as infinite series of hypergeometric functions.…
We describe, in some detail, a number of different Coulomb gas formulations of $N=2$ superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg…
Although it is well-known that the complex cobordism ring is a polynomial ring $\Omega_{*}^{U}\cong\mathbb{Z}\left[\alpha_{1},\alpha_{2},\ldots\right]$, an explicit description for convenient generators $\alpha_{1},\alpha_{2},\ldots$ has…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
We calculate the two-loop QCD corrections to $gg \to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we…
A hierarchy of $\mathbb{Z}_2^2$-graded integrable equations is constructed using the loop extension of the $\mathbb{Z}_2^2$-graded Lie superalgebra $\mathfrak{osp}(1|2)$. This hierarchy includes $\mathbb{Z}_2^2$-graded extensions of the…
This paper describes the $K$-theory structure for three algebra classes. For cyclic $p$-group rings and truncated polynomial rings over $\mathbb{Z}/p^s\mathbb{Z}$, we determine reduced $K_2$-structures via a common algebraic framework. For…
To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion…
The full two-loop amplitudes for five massless states in Type~II and Heterotic superstrings are constructed in terms of convergent integrals over the genus-two moduli space of compact Riemann surfaces and integrals of Green functions and…
Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic…
Using skein valued holomorphic curve counting techniques, we give a flow loop formula for the skein valued partition function of the Lagrangian knot complement of a fibered knot (of the $A$-model open topological strings with Lagrangian…
The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras constructed through abelian extensions of $Z_2$ for an abelian group $G$. We prove that there are only two forms of them. Using such…
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
We study the quantum open system evolution described by a Gorini-Kossakowski-Sudarshan-Lindblad generator with creation and annihilation operators arising in Fock representations of the $sl_2$ Lie algebra. We show that any initial density…
We introduce an algebra bundle of chord diagrams over the configuration space of N points in the complex plane on which we put the Knizhnik-Zamolodchikov connection. For that particular connection, the holonomy along a loop in the base is…
The paper aims at constructing two different solutions to an elliptic system $$ u \cdot \nabla u + (-\Delta)^m u = \lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers…
We consider Dotsenko-Fateev matrix models associated with compactified Calabi-Yau threefolds. They can be constructed with the help of explicit expressions for refined topological vertex, i.e. are directly related to the corresponding…
We consider the qKZ equations based on the two boundaries Temperley Lieb algebra. We construct their solution in the case $s=q^{-3/2}$ using a recursion relation. At the combinatorial point $q^{1/2}= e^{-2\pi i/3}$ the solution reduces to…
We evaluate string one-loop contributions to the Einstein-Hilbert term in toroidal minimally supersymmetric type IIB orientifolds with D-branes. These have potential applications to the determination of quantum corrections to the moduli…