MS Seminar (Mathematics - String Theory)

Speaker: Jie-qiang Wu (Peking U)
Title: Entanglement entropy and higher genus partition function in AdS_3/CFT_2
Date (JST): Tue, Apr 26, 2016, 13:15 - 14:30
Place: Seminar Room A
Related File: 1690.pdf
Abstract: The AdS_3/CFT_2 correspondence is a good arena for AdS/CFT correspondence. We have a good understanding in both gravity and the field theory side. On the other hand the holographic entanglement entropy draw a lot of attention from different field including high energy physics and condensed matter physics. It shows a connection between geometry and quantum information. In this work we will use the entanglement entropy as a measure to check AdS_3/CFT_2. In this talk I will first give a brief introduction for AdS_3/CFT_2 and holographic entanglement entropy.
Then I will introduce our work on the finite temperature entanglement entropy in AdS_3/CFT_2 system. We calculate the entanglement entropy in both the field theory side and the gravity side. In field theory side, by replica trick the R\'enyi entropy calculation transform to partition function on higher genus Riemann surface, and we use sewing prescription to calculate it order by order with respect to some parameter related to the system. In gravity we study holographic R\'enyi entropy and calculate the 1-loop quantum correction on this background. We find agreement between field theory and gravity to some higher order in high/low temperature, large/small interval. We also study the phase transition in this system in field theory and in gravity. The correspondence strongly support the AdS_3/CFT_2 correspondence.
Furthermore I will give a general calculation for the partition function on higher genus Riemann surface. In large central charge limit, the calculation is simplified and behave like a free theory. We calculate the $c^0$ order partition function and find agreement with holographic calculation.