# Gravity Amplitudes as Generalized Double Copies

## TL;DR

This paper introduces a modified double-copy method to derive gravity integrands from generic gauge-theory integrands, including contact terms, without requiring manifest BCJ duality, demonstrated through high-loop examples in supergravity.

## Contribution

It presents a new approach to obtain gravity integrands from non-manifest gauge-theory integrands, expanding the applicability of the double-copy procedure at high loop orders.

## Key findings

- Successfully applied to three-, four-, and five-loop examples in N=8 supergravity.
- Generated contact terms from violations of dual Jacobi identities.
- Demonstrated that the method works without manifest BCJ duality.

## Abstract

Whenever the integrand of a gauge-theory loop amplitude can be arranged into a form where the BCJ duality between color and kinematics is manifest, a corresponding gravity integrand can be obtained simply via the double-copy procedure. However, finding such gauge-theory representations can be challenging, especially at high loop orders. Here we show that we can instead start from generic gauge-theory integrands, where the duality is not manifest, and apply a modified double-copy procedure to obtain gravity integrands that include contact terms generated by violations of dual Jacobi identities. We illustrate this with three-, four- and five-loop examples in N=8 supergravity.