High Energy Theory Seminar

In the first part we discuss the holographic entanglement entropy in AdS4/CFT3 for finite domains with generic shapes. For smooth shapes the constant term can be evaluated by employing a generalisation of the Willmore functional for two dimensional surfaces. Explicit examples are given for asymptotically AdS4 black holes, domain wall geometries and time dependent backgrounds.
The second part is focused on the entanglement negativity in CFT. In 2+1 dimensions we present some numerical results for two adjacent regions in a two dimensional harmonic lattice. In 1+1 dimensions and for two disjoint intervals in the Ising and the Dirac fermion models, we show that the contribution of a given spin structure to the CFT expression of the moments of the partial transpose is obtained as the scaling limit of a specific lattice term. This analysis provides also the moments of the partial transpose for the free fermion.