Absence of Three-Loop Four-Point Divergences in N=4 Supergravity

TL;DR

This paper demonstrates that the three-loop four-point divergence in pure N=4 supergravity vanishes, challenging previous expectations and suggesting deeper cancellations possibly extending to higher loops.

Contribution

The authors explicitly compute and show the absence of the three-loop divergence in N=4 supergravity using color-kinematics duality, revealing unexpected all-loop cancellations.

Findings

Three-loop divergence coefficient is zero.

Color-kinematics duality simplifies complex calculations.

Hints of further cancellations at higher loops.

Abstract

We compute the coefficient of the potential three-loop divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments. The recently uncovered duality between color and kinematics is used to greatly streamline the calculation. We comment on all-loop cancellations hinting at further surprises awaiting discovery at higher loops.