Related papers: Two dialects for KZB equations: generating one-loo…
The Remodeling Conjecture proposed by Bouchard-Klemm-Mari\~{n}o-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (open and closed Gromov-Witten invariants) of a symplectic toric Calabi-Yau 3-fold to…
In a previous work, we gave a coalgebraic framework of directed graphs equipped with weights (or probability vectors) in terms of (Markov) L-coalgebras. They are K-vector spaces equipped with two co-operations, \Delta_M, \tilde{\Delta}_M…
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decoupled $\beta$-$\gamma$ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an…
We revisit the evaluation of one-loop modular integrals in string theory, employing new methods that, unlike the traditional 'orbit method', keep T-duality manifest throughout. In particular, we apply the Rankin-Selberg-Zagier approach to…
We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives…
We propose a new construction of vertex operators of the elliptic quantum toroidal algebra $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ by combining representations of the algebra and formulas of the elliptic stable envelopes for the…
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial…
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it…
We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix…
We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations…
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of…
We study topological strings on local toric del Pezzo surfaces by a method called remodeling the B-model which was recently proposed by Bouchard, Klemm, Marino and Pasquetti. For a large class of local toric del Pezzo surfaces we prove a…
It is shown that several of Brafman's generating functions for the Gegenbauer polynomials are algebraic functions of their arguments, if the Gegenbauer parameter differs from an integer by one-fourth or one-sixth. Two examples are given,…
The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…
It is shown that the sl(2,C) KZ equation for (half-) integer isospins recovers, up to a gauge transformation, the matrix system for Virasoro algebra singular vectors of Bauer et al. In the case of Kac-Kazhdan spins the general (infinite…
A new orientifold of Type-IIB theory on $K3$ is constructed that has $N=1$ supersymmetry in six dimensions. The orientifold symmetry consists of a $Z_2$ involution of $K3$ combined with orientation-reversal on the worldsheet. The…
An algebraic interpretation of the one-variable quantum $q$-Krawtchouk polynomials is provided in the framework of the Schwinger realization of $\mathcal{U}_{q}(sl_{2})$ involving two independent $q$-oscillators. The polynomials are shown…
Several aspects of (0,2) Landau-Ginzburg orbifolds are investigated. Especially the elliptic genera are computed in general and, for a class of models recently invented by Distler and Kachru, they are compared with the ones from (0,2) sigma…
We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…
The construction of $SL(2,Z)$ invariant amplitudes that generalizethe Virasoro amplitude is investigated in detail. We describe a number of mathematical properties that characterize the simplest example, and present pieces of evidence that…