Related papers: Towards a Loop-Tree Duality at Two Loops and Beyon…
Various examples of target space duality transformations are investigated up to two loop order in perturbation theory. Our results show that when using the tree level (`naive') transformation rules the dual theories are in general {\it…
Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the…
We derive a variant of the loop-tree duality for Feynman integrals in the Schwinger parametric representation. This is achieved by decomposing the integration domain into a disjoint union of cells, one for each spanning tree of the graph…
We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which…
Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases…
We show how Stone duality can be extended from maps to relations. This is achieved by working order enriched and defining a relation from A to B as both an order-preserving function from the opposite of A times B to the 2-element chain and…
We find that scattering amplitudes in massive scalar QCD can manifest the duality between color and kinematics at loop-level. Specifically we construct the one-loop integrands for four-point scattering between two distinct massive scalars,…
We present an overview of the analysis of the multiloop topologies that appear for the first time at four loops and the assembly of them in a general expression, the N$^4$MLT universal topology. Based on the fact that the Loop-Tree Duality…
We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged…
Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the…
Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one…
We study double copy relations for loop integrands in gauge theories and gravity based on their constructions from single cuts, which are in turn obtained from forward limits of lower-loop cases. While such a construction from forward…
Colour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar…
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…
This thesis presents a thorough analysis of the links between the N=4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in deriving explicit results in terms of the vacuum…
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
In this article we review a recent calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. Using the effective action approach, and focusing on backgrounds with a single Abelian isometry, we give the…
We continue the study of n-point correlation functions of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the l-loop corrections…
The spinor-helicity formalism has proven to be very efficient in the calculation of scattering amplitudes in quantum field theory, while the loop tree duality (LTD) representation of multi-loop integrals exhibits appealing and interesting…
We report on a new method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…