# Two-Loop Renormalization of Quantum Gravity Simplified

## TL;DR

This paper simplifies the understanding of two-loop renormalization in quantum gravity by showing that evanescent operators do not affect physical scattering amplitudes, using unitarity cuts in four dimensions.

## Contribution

It provides a method to analyze two-loop quantum gravity renormalization without relying on evanescent operators, clarifying their non-physical role.

## Key findings

- Evanescent operators do not influence physical scattering amplitudes.
- The two-loop four-graviton amplitude's dependence on the renormalization scale is straightforward.
- Unitarity cuts in four dimensions suffice for analysis, avoiding evanescent operators.

## Abstract

The coefficient of the dimensionally regularized two-loop R^3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced by the anti-symmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences in renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. In this paper, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.