HEP Theory Journal Club

Holographic description of entanglement entropy and conformal block in AdS₃/CFT₂

Jie-Qiang Wu

Peking University

AdS₃/CFT_{2 is a good arena to study holography. In this work, we focus on two dimensional conformal field theory. In semi-classical limit, the conformal block can be studied by solving a monodromy problem. We extend this technic to more general case to study entanglement entropy and heavy operator conformal block.}

For entanglement entropy, we use the monodromy trick to study the entanglement for a general class of states. We found the final result is consistent with Ryu-Takayanagi formula. Actually, in gravity side, if we use Chern-Simons form, there is direct correspondence with the field theory calculation.

For the heavy operator conformal block, we expect it should dual to an on-shell action in gravity with conical defects. In gravity side, if we take a variation with respect to the conical angle, we get the length of conical defect. In field theory side, it implies by taking a variation with conformal dimension, we get a quantity which dual to length of conical defect. We prove this relation in CFT₂. It is a strong support for the holographic description of conformal block.