# Manifesting enhanced cancellations in supergravity: integrands versus integrals

## TL;DR

This paper investigates the nature of enhanced ultraviolet cancellations in supergravity, demonstrating that such cancellations are not apparent before integration and are linked to symmetries like Lorentz and SL(L), with implications for understanding finiteness.

## Contribution

It shows that enhanced cancellations in supergravity cannot be seen prior to integration and that symmetries like Lorentz and SL(L) explain these cancellations at multiple loops.

## Key findings

- Enhanced cancellations are not manifest before integration.
- Integral identities from symmetries explain cancellations at two loops.
- SL(L) symmetry suffices to display cancellations up to (L-1) loops.

## Abstract

Examples of "enhanced ultraviolet cancellations" with no known standard-symmetry explanation have been found in a variety of supergravity theories. By examining one- and two-loop examples in four- and five-dimensional half-maximal supergravity, we argue that enhanced cancellations in general cannot be exhibited prior to integration. In light of this, we explore reorganizations of integrands into parts that are manifestly finite and parts that have poor power counting but integrate to zero due to integral identities. At two loops we find that in the large loop-momentum limit the required integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry out a nontrivial check at four loops showing that the identities generated in this way are a complete set. We propose that at $L$ loops the combination of Lorentz and SL($L$) symmetry is sufficient for displaying enhanced cancellations when they happen, whenever the theory is known to be ultraviolet finite up to $(L-1)$ loops.