# Two-loop n-point anomalous amplitudes in N=4 supergravity

## TL;DR

This paper calculates the first two-loop n-point anomalous amplitudes in N=4 supergravity, revealing their structure, the effect of counterterms, and implications for finiteness at higher loops.

## Contribution

It presents the first computation of two-loop n-point gravity amplitudes in N=4 supergravity, including all terms from four-dimensional cuts and analysis of counterterm effects.

## Key findings

- First two-loop n-point anomalous supergravity amplitudes computed.
- Counterterm cancels these amplitudes at this order.
- Three-loop finiteness of anomalous amplitudes remains unaffected.

## Abstract

We compute the anomalous two-loop four-point amplitudes in N=4 pure supergravity, using unitarity and the double-copy construction. We also present all terms determined by four-dimensional cuts in two all-multiplicity two-loop anomalous superamplitudes. This result provides the first two-loop n-point gravity amplitude, up to a class of undetermined rational terms, which are absent at four points. We show that a recently proposed finite counterterm cancels these amplitudes to this order. We argue that the counterterm does not spoil the three-loop finiteness of anomalous amplitudes in the N=4 theory.