Locally Finite Observables in sYM

TL;DR

This paper proves that all two-loop ratio functions in planar maximally supersymmetric Yang-Mills theory are locally-finite, meaning they have no divergences in the space of real loop momenta and can be computed without regularization.

Contribution

It establishes the local finiteness of all two-loop ratio functions in planar maximally supersymmetric Yang-Mills theory, a significant step in understanding their divergence structure.

Findings

All two-loop ratio functions are locally-finite.

No divergences occur in the space of real loop momenta for these functions.

They can be computed without regularization.

Abstract

A `locally-finite' observable is one for which there is no region of divergence anywhere in the space of real loop momenta; it can therefore be computed (in principle) without regularization. In this work, we prove that all two-loop ratio functions in planar, maximally supersymmetric Yang-Mills theory are locally-finite.