Supersymmetric Lagrangians

Let’s recall some notions from classical Lagrangian field theory. Let M be an oriented supermanifold: our spacetime, of dimension n|d. For our purposes, we will most often think about the case where M is either Minkowski space M̌ = R1,n−1, or Super Minkowski space M = M̌ ×ΠS where S is a representation of Spin(1, n− 1). Definition 1.1. Let E → M be a smooth (super) fibre bundle. The associated space of fields is the space of smooth sections φM → E. A Lagrangian density on F is a function L : F → Dens(M) – where Dens(M) denotes the bundle of densities on M – that satisfies a locality condition.