Protected Observables in Supersymmetric Theories as a Probe of Entanglement

The study of entanglement plays a central role in understanding quantum many body systems. However, quantitative measures of entanglement such as the entanglement entropy of the groundstate are hard to compute except in the simplest systems. Supersymmetric theories (SUSY) famously admit observables such as the Witten index which are invariant under SUSY preserving deformations and can be computed by localisation. They also often exhibit large degeneracies and an accompanying Hilbert space of zero energy (or more generally SUSY preserving) groundstates. In this project we will attempt to formulate and compute observables which measure the entanglement of states in this subspace.