Related papers: Asyzygies, modular forms, and the superstring meas…
We compute one-loop amplitudes in six-dimensional Yang-Mills theory with half-maximal supersymmetry from first principles: imposing gauge invariance and locality on an ansatz made from string-theory inspired kinematic building blocks yields…
We calculate the three loop anomalous dimension for a general $N=1$ supersymmetric gauge theory. The result is used to probe the possible existence of renormalisation invariant relationships between the Yukawa and gauge couplings.
An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted…
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
Let $K$ denote a simply connected compact Lie group and let $G=K^{\mathbb C}$, the complexification. It is known that there exists an $LK$ bi-invariant probability measure on a natural hyperfunction completion of the complex loop group…
The inverse amplitude method is analysed to two-loop order in the chiral expansion in the case of $\pi\pi$ scattering and the pion form factors. The analysis is mainly restricted to the elastic approximation but the possible extension to…
We construct a superpotential for the general N=1/2 supersymmetric gauge theory coupled to chiral matter in the adjoint representation, and investigate the one-loop renormalisability of the theory.
The slice-independent gauge-fixed superstring chiral measure in genus 2 derived in the earlier papers of this series for each spin structure is evaluated explicitly in terms of theta-constants. The slice-independence allows an arbitrary…
Superstring amplitudes of an arbitrary genus are calculated through super-Schottky parameters by a summation over the fermion strings. For a calculation of divergent multi-loop fermion string amplitudes a supermodular invariant…
Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…
We give a brief review of our approach to the quantization of superstrings. New is a covariant derivation of the measure at tree level and a path integral formula for this measure.
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in "Log-sine evaluations of Mahler measures" and "Special values of generalized log-sine integrals" by two of the authors. This motivates a…
In this paper we propose a new version for the noncommutative superspace in 3D. This version is shown to be convenient for performing quantum calculations. In the paper, we use the theory of the chiral superfield as a prototype for possible…
We study a new mechanism for the electromagnetic gauging of chiral bosons showing that new possibilities emerge for the interacting theory of chiral scalars. We introduce a chirally coupled gauge field necessary to mod out the degree of…
I present analytical expressions for the cusp anomalous dimension in QCD through three loops in terms of elementary functions and ordinary polylogarithms. I observe interesting relations between the results at different loops and provide a…
Based on the recent developments of explicit computations at 2 loops in superstring theory in the covariant RNS formalism, we propose an explicit formula for the arbitrary loop 4-particle amplitude in superstring theory. We prove that this…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
Chiral gauge theories in two dimensions with (0,2) supersymmetry are central in the study of string compactifications. Remarkably little is known about generic (0,2) theories. We consider theories with branches on which multiplets with a…
We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…
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…