Covariant procedures for perturbative nonlinear deformation of duality-invariant theories

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.

Non-renormalization for non-supersymmetric black holes

“…We will also discuss higher-derivative correction to Einstein-Maxwell theory in C.1.1, explaining along the way how our results are consistent with earlier work regarding the duality-invariant deformations of Maxwell theory with higher order terms, such as [47][48][49]. The derivation leading to (4.17) is a slight generalization of the derivation in appendix B of [16].…”

“…These are given, respectively, by 48) which are precisely the Lagrangians presented in (3.12) and (3.25).…”

“…also need to add an infinite amount of higher order terms F 2n for all n > 2 [47][48][49]. One possible way of doing so is Born-Infeld theory…”

“…There are other non-equivalent ways to deform the Maxwell Lagrangian in a way consistent with duality symmetry [48].…”

N=2 supergravity counterterms, off and on shell

“…However in [18] it was suggested that one can restore duality invariance of the full theory by adding an infinite number of additional terms to the theory. This implies that instead of the original version of the theory one should construct its Born-Infeld type generalization [19][20][21]. While this generalization can indeed be constructed for N = 2, as we will show in this paper, it is not known how to generalize this restoration of duality for N = 4, 8.…”