Related papers: Towards a categorification of scattering amplitude…
We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructing a quiver with potential. The rank of the cluster algebra…
Supergravity theories with non-minimal K\"ahler potentials are characterized by a non-trivial field space manifold with corresponding non-trivial kinetic terms. The scattering amplitudes in these theories can be calculated at fixed…
We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the…
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests…
I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…
Plabic graphs are intimately connected to the positroid stratification of the positive Grassmannian. The duals to these graphs are quivers, and it is possible to associate to them cluster algebras. For the top-cell graph of $Gr_{+}(k,n)$,…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
We introduce Feynman-like rules to compute quivers for two loops and higher for the coloured planar $\phi^3$ theory for winding number zero. We demonstrate this for a few cases. Then we extend this further to the case of $\phi^n$ theories,…
Multiple scattering theory is applied to the study of clusters of point-like scatterers attached to a thin elastic plate and arranged in quasi-periodic distributions. Two type of structures are specifically considered: the twisted bilayer…
A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking,…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
In this paper, the approach for considering fast charged particles scattering on targets of complex structure, which contains some isolated substructures, was expanded to account quadratic potential terms. Based on this approach, the…
One of the main challenges in obtaining predictions for collider experiments from perturbative quantum field theory, is the direct evaluation of the Feynman integrals it gives rise to. In this chapter, we review an alternative bootstrap…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…
Multi-channel phase space with a single Feynman diagram enhancement is a powerful tool for high-energy physics event generation if a diagram with a singular propagator dominates the total scattering amplitude at the corresponding singular…
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster…
We introduce and study potentials, mutations and Jacobian algebras in the framework of tensor algebras associated with symmetrizable dualizing pairs of bimodules on a symmetric algebra over any commutative ground ring. The graded context is…
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…
We describe in detail the techniques needed to compute scattering amplitudes for colored scalars from the infinite tension limit of bosonic string theory, up to two loops. These techniques apply both to cubic and quartic interactions, and…