Anomalies and divergences in N=4 supergravity

TL;DR

This paper investigates the potential divergences in N=4 supergravity at three loops, focusing on the role of anomalies and duality invariance, and concludes that certain marginal invariants cannot serve as counterterms under specific assumptions.

Contribution

It provides a detailed analysis of three-loop divergences in N=4 supergravity, highlighting the impact of anomalies and the constraints imposed by duality and supersymmetry.

Findings

Duality invariance constrains three-loop counterterms.

Marginal invariants are not allowed as counterterms under full off-shell formalism.

Anomalies affect the symmetry restrictions on divergences.

Abstract

The invariants in D=4, N=4 supergravity are discussed up to the three-loop order (where one expects a general R^4 structure). Because there is an anomaly in the rigid SL(2,R) symmetry of this theory, the analysis of possible restrictions on three-loop divergences due to duality needs careful treatment. We show that this anomalous symmetry is still strong enough at the three-loop order to require duality invariance of candidate counterterms. Provided one makes the additional assumption that there exists a full 16-supercharge off-shell formulation of the theory, counterterms at L \ge 2 loops would also have to be writable as full-superspace integrals. At the three-loop order such a duality-invariant full-superspace integral candidate counterterm exists, but its duality invariance is marginal in the sense that the full-superspace counter-Lagrangian is not itself duality invariant. We show that, subject to the assumption that a full off-shell quantisation formalism exists, such marginal invariants are not allowable as counterterms.