On duality symmetries of supergravity invariants

TL;DR

This paper investigates how duality symmetries influence the construction of counterterms in maximal supergravity theories, providing proofs of invariance constraints and finiteness at certain loop orders.

Contribution

It introduces new methods to analyze duality invariance of supergravity counterterms, proving non-invariance of certain F-term counterterms and finiteness of specific supergravity theories.

Findings

F-term counterterms cannot be E7(7)-invariant in D=4, N=8 supergravity.

N=6 supergravity is finite at three and four loops.

N=5 supergravity is finite at three loops.

Abstract

The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. The former allows us to prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8 supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed by the two other methods which can also be applied to D=4 theories with fewer supersymmetries and allow us to prove that N=6 supergravity is finite at three and four loops and that N=5 supergravity is three-loop finite.