Counterterms vs. Dualities

TL;DR

This paper explores how higher order corrections in supergravity and string theory can be made compatible with duality symmetries, providing a method to incorporate duality-invariant counterterms into the effective action.

Contribution

It introduces a systematic approach to include duality-invariant counterterms in effective actions, ensuring compatibility with non-linear duality symmetries and diffeomorphism invariance.

Findings

Demonstrates how to incorporate duality-invariant counterterms into the action.

Shows the procedure for Maxwell theory counterterms like R^2 ∇F ∇F and F^4.

Provides a consistency framework for maintaining duality and diffeomorphism invariance.

Abstract

We investigate and clarify the mutual compatibility of the higher order corrections arising in supergravity and string theory effective actions and the non-linear duality symmetries of these theories. Starting from a conventional tree level action leading to duality invariant equations of motion, we show how to accommodate duality invariant counterterms given as functionals of both electric and magnetic fields in a perturbative expansion, and to deduce from them a non-polynomial bona fide action satisfying the Gaillard-Zumino constraint. There exists a corresponding consistency constraint in the non-covariant Henneaux-Teitelboim formalism which ensures that one can always restore diffeomorphism invariance by perturbatively solving this functional identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F and F^4 counterterms in Maxwell theory.