Integration-by-parts identities in FDR

TL;DR

This paper demonstrates that integration-by-parts identities can be applied to four-dimensional renormalized (FDR) integrals, enabling more efficient multi-loop calculations without UV counterterms.

Contribution

It proves that IBP identities can relate multi-loop FDR integrals, advancing the use of FDR in complex loop computations.

Findings

IBP identities are applicable to FDR integrals

Enables multi-loop FDR calculations without UV counterterms

Facilitates the use of IBP algorithms in FDR context

Abstract

Four-dimensional renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet (UV) counterterms. In this paper I prove that integration-by-parts (IBP) identities can be used to find relations among multi-loop FDR integrals. Since algorithms based on IBP are widely applied beyond one loop, this result represents a decisive step forward towards the use of FDR in multi-loop calculations.