Majorana Fermions, Supersymmetry Breaking, and Born-Infeld Theory

This review is devoted to highlight some aspects of the relevance of Majorana fermions in rigid supersymmetry breaking in four spacetime dimensions. After introducing some basic: facts on spinors, and on their symmetries and reality properties, we consider Goldstino actions describing partial breaking of rigid supersymmetry, then focussing on Born-Infeld non-linear theory, its duality symmetry, and its supersymmetric: extensions, also including multi-field generalizations exhibiting doubly self-duality.