We compute the holographic entanglement entropy for the pure gravitational anomaly in 3+1 dimensions. Using the perturbative method developed for com- puting entanglement entropy for quantum field theories, we also compute the parity odd contribution to the entanglement entropy of the dual field theory that comes from a background gravitational Chern-Simons term. We find that, in leading order in the perturbation of the background geometry, the two contribu- tions match except for a logarithmic divergent term on the field theory side. We interpret this extra contribution as encoding our ignorance of the source which creates the perturbation of the geometry.

Quantum field theories in (2+1)-dimensions exhibit a beautiful property known as particle-vortex duality. It relates, in a precise way, two different excitations on the plane, the familiar particle-like excitations that arise from quantisation of the field and vortices, solitonic-excitations defined by the winding of a local order parameter. Originally studied in the context of anyonic superconductivity and Neilsen-Olesen vortices, extensions of the duality have recently found application to, for example, topological quantum matter. I will review some of these developments and show how recent progress in understanding non-abelian T-duality can be used to define a non-abelian particle-vortex duality in (2+1)-dimensions.