Related papers: CHY-Graphs on a Torus
We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for…
We present the complete one-loop calculation of all the two meson scattering amplitudes within the framework of SU(3) Chiral Perturbation Theory, which includes pions, kaons and the eta. In addition, we have unitarized these amplitudes with…
We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
Moir\'e flatbands with high Chern numbers (C>1) offer opportunities to study the fractional quantum anomalous Hall effects that go beyond the Landau level paradigm with C=1, which remain unexplored yet. Here, we target the novel topological…
We study a complex analogue of a Wilson Loop, defined over a complex curve, in non-Abelian holomorphic Chern-Simons theory. We obtain a version of the Makeenko-Migdal loop equation describing how the expectation value of these Wilson Loops…
The topological quantum number Q of a superconducting or chiral insulating wire counts the number of stable bound states at the end points. We determine Q from the matrix r of reflection amplitudes from one of the ends, generalizing the…
Using the {\em cutting and sewing} procedure we show how to get Feynman diagrams, up to two-loop order, of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a…
So-called `non-factorisable' toroidal orbifolds can be rewritten in a factorised form as a product of three two-tori by imposing an additional shift symmetry. This finding of Blaszczyk et al., arXiv:1111.5852, provides a new avenue to…
We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…
Recent experiments observed fractional Chern insulators (FCI) in twisted bilayer MoTe$_2$ at zero magnetic field, yet even the single-particle model of this material is controversial, leading to unreliable predictions of the experimental…
The {\em cutting and sewing} procedure is used for getting two-loop order Feynman diagrams of $\Phi^{4}$-theory with an internal SU(N) symmetry group, starting from tachyon amplitudes of the open bosonic string theory. In a suitably defined…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This…
Feynman integrals in quantum field theory evaluate to special functions and numbers that are usefully described by the notion of transcendental weight. In this paper, we propose a way of projecting a given dimensionally-regularised Feynman…
The derivative expnsion in the context of IIB string scattering compactified on non-trivial K3 and other Calabi-Yau manifolds is formulated. The scattering data in terms of automorphic functions can be inverted to find the these metrics.…
We address the analytic computation of the two-loop scattering amplitudes for the production of two photons in parton-parton scattering, mediated by loops of heavy quarks. Due to the presence of integrals of elliptic type, both partonic…
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several…
We find a direct map that determines moduli-space integrands for one-loop superstring amplitudes in terms of field-theory loop integrands in the BCJ form. The latter can be computed using efficient unitarity methods, so our map provides an…
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of…
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…