Nonlinear Self-Duality and Supersymmetry

TL;DR

This paper reviews the concept of self-duality in nonlinear electrodynamics and supersymmetric models, discusses the self-duality equations and solutions, and examines the correctness of proposed supersymmetric actions for D3 branes.

Contribution

It provides a comprehensive review of self-duality in nonlinear and supersymmetric gauge theories, including derivation of self-duality equations and analysis of supersymmetric D3 brane actions.

Findings

Self-duality equations are derived and solutions discussed.

Born-Infeld action is a key example of self-dual nonlinear electrodynamics.

Existing N=2 supersymmetric actions for D3 branes are shown to be incorrect.

Abstract

We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. We then describe self-duality in supersymmetric models, both N = 1 and N = 2. The self-duality equations, which have to be satisfied by the action of any self-dual system, are found and solutions are discussed. One important example is the Born-Infeld action. We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6.