Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

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, discussing the area law behaviour and the
corner contributions. 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 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.