Covariant procedures for perturbative non-linear deformation of duality-invariant theories

TL;DR

This paper investigates a perturbative method to construct non-linear, duality-invariant theories like Born-Infeld, starting from initial deformations and extending to supersymmetric theories, with implications for supergravity finiteness.

Contribution

It introduces a covariant, perturbative procedure to generate non-linear duality-invariant deformations, including Born-Infeld, for various supersymmetric theories and supergravity.

Findings

Constructed a non-linear deformation procedure for duality-invariant theories.

Extended the method to N=1 and N=2 supersymmetric theories.

Discussed implications for supergravity finiteness and theory construction.

Abstract

We analyze a recent conjecture regarding the perturbative construction of non-linear deformations of all classically duality invariant theories, including N=8 supergravity. Starting with an initial quartic deformation, we engineer a procedure that generates a particular non-linear deformation (Born-Infeld) of the Maxwell theory. This procedure requires the introduction of an infinite number of modifications to a constraint which eliminates degrees of freedom consistent with the duality and field content of the system. We discuss the extension of this procedure to N=1 and N=2 supersymmetric theories, and comment on its potential to either construct new supergravity theories with non-linear Born-Infeld type duality, or to constrain the finiteness of N=8 supergravity.