Doubly Self-Dual Actions in Various Dimensions

TL;DR

This paper explores the concept of double self-duality in non-linear actions involving form pairs across various dimensions, extending known supersymmetric dualities and introducing a new U(1) invariant Born-Infeld generalization.

Contribution

It generalizes the self-duality phenomenon to D dimensions for form pairs and constructs a novel two-field Born-Infeld type action with U(1) duality invariance.

Findings

Extended double self-duality to D dimensions for form pairs.

Constructed a new two-field Born-Infeld action with U(1) invariance.

Introduced Green-Schwarz terms leading to mass-like dual pairs.

Abstract

The self-duality of the N=1 supersymmetric Born--Infeld action implies a double self-duality of the tensor multiplet square-root action when the scalar and the antisymmetric tensor are interchanged via Poincare' duality. We show how this phenomenon extends to D space-time dimensions for non-linear actions involving pairs of forms of rank p and D-p-2. As a byproduct, we construct a new two-field generalization of the Born-Infeld action whose equations of motion are invariant under a U(1) duality. In these systems, the introduction of Green-Schwarz terms results in explicit non-linear mass-like terms for dual massive pairs.