GP seminar: Entanglement Asymmetry

Abstract: Entanglement Asymmetry is a tool to quantify symmetry breaking in states. It's a relative entropy between a given state and a symmetrized version thereof. I will first, for groups, discuss how this can be computed in a CFT via replica path integrals. Next, we will move to the case of non-invertible symmetries. We will see the different symmetry algebras that emerge from the action of an underlying fusion category on a Hilbert space. Exploiting a special property common to these algebras, we will find the general recipe to symmetrize a state with respect to any symmetry. We will see come examples in CFTs as well as TQFTs. Based on elements of https://arxiv.org/abs/2509.16311.

If time permits, I will briefly discuss asymmetry in the context of AdS/CFT (https://arxiv.org/abs/2407.07969).

This is a seminar in the Centre of Geometry and Physics seminar series.