Topological Entanglement Entropy and Holography

Understand

We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi.

• The entanglement entropy between a region and its complement is proportional to the minimal area of a bulk hypersurface ending on their border.
• We consider a disk in 2+1 dimensions and a ball in 3+1 dimensions and find in both cases two types of bulk hypersurfaces with different topology, similar to the case of the slab geometry considered by Klebanov, Kutasov and Murugan.
• Depending on the value of the radius, one or the other type of hypersurfaces dominates the calculation of entanglement entropy.