Related papers: Open-string integrals with multiple unintegrated p…
We study a family of generalized hypergeometric integrals defined on punctured Riemann surfaces of genus g. These integrals are closely related to g-loop string amplitudes in chiral splitting, where one leaves the loop-momenta, moduli and…
We study integrals appearing in one-loop amplitudes in string theory, and in particular their analytic continuation based on a string theoretic analog of the $i\varepsilon$-prescription of quantum field theory. For various zero- and…
In this paper, we introduce a class of twisted matrix algebras of $M_2(E)$ and twisted direct products of $E\times E$ for an algebra $E$. Let $A$ be a noetherian Koszul Artin-Schelter regular algebra, $z\in A_2$ be a regular central element…
Multiloop superstring amplitudes are calculated in the explicit form by the solution of Ward identities. A naive generalization of Belavin-Knizhnik theorem to the superstring is found to be incorrect since the period matrix turns out to be…
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…
Amplitudes in open topological string theory may be described completely by certain A-infinity-categories. We detail a general construction of all cyclic minimal models for a given A-infinity-algebra and apply this result to the case of N=2…
We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra…
We count the number of bound states of BPS black holes on local Calabi-Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang-Mills theory on the Riemann…
In this Letter, we provide evidence for a new double-copy structure in one-loop amplitudes of the open superstring. Their integrands with respect to the moduli space of genus-one surfaces are cast into a form where gauge-invariant kinematic…
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…
In this paper we study the Brauer loop model on a strip and the associated quantum Knizhnik--Zamolodchikov (qKZ) equation. We show that the minimal degree solution of the Brauer qKZ equation with one of four different possible boundary…
We review a novel method for evaluating one-loop BPS-saturated amplitudes in string theory. Contrary to traditional techniques of unfolding the fundamental domain F against the Narain lattice, which are only valid in certain regions of the…
After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus $h\leq 3$ are reduced to an integral of a Siegel modular function of degree $h$ on a fundamental domain of the Siegel…
We develop an algebraic representation for (1,1)-knots using the mapping class group of the twice punctured torus MCG(T,2). We prove that every (1,1)-knot in a lens space L(p,q) can be represented by the composition of an element of a…
Perturbative spectra and related factorization properties of one-loop open string amplitudes in the presence of a constant external background B are analysed in detail. While the pattern of the closed string spectrum, obtained after a…
In this text we review various relations between building blocks of closed and open string amplitudes at tree-level and genus one. We explain that KLT relations between tree-level closed and open string amplitudes follow from the…
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly…
In this paper, we give the general expressions for a special series of tree amplitudes of the Yang-Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive…
The string-based Bern-Kosower rules provide an efficient way for obtaining parameter integral representations of the one-loop N - photon/gluon amplitudes involving a scalar, spinor or gluon loop, starting from a master formula and using a…
We describe the lower algebraic $K$-theory of the integral group ring of both the pure and full braid groups of the real projective plane $\mathbb{R}P^2$ with $3$ strings, as well as that of the integral group ring of the mapping class…