Local renormalisation from causal loop-tree duality

TL;DR

This paper introduces a novel local renormalisation approach based on causal loop-tree duality, successfully cancelling UV divergences up to three loops and enabling numerical simulations without dimensional regularisation.

Contribution

It develops a new formalism for local renormalisation using causal loop-tree duality, applicable in four dimensions and suitable for numerical implementation.

Findings

Successfully cancels UV divergences up to three loops

Produces more compact expressions with desirable properties

Enables smooth numerical implementation in four dimensions

Abstract

We report recent progress on the development of a local renormalisation formalism based on causal loop-tree duality (cLTD). By performing an expansion around the UV-propagator in an Euclidean space, we manage to build counter-terms to cancel the non-integrable terms in the UV limit. This procedure is then combined with the so-called causal representation, and the UV expansion is performed at the level of on-shell energies. The resulting expressions are more compact, and they retain nice properties of the original causal representation. The proposed formalism is tested up to three-loops, with relevant families of topologies. In all the cases, we successfully cancel the UV divergences and achieve a smooth numerical implementation. These results constitute a first step towards a new renormalisation program in four space-time dimensions (by-passing DREG), perfectly suitable for fully numerical simulations.