Holographic Calculation for Large Interval R\'enyi Entropy at High Temperature

Understand

In this paper, we study the holographic R\'enyi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS$_3$ gravity.

• In the field theory, the R\'enyi entropy is encoded in the CFT partition function on $n$-sheeted torus connected with each other by a large branch cut.
• As proposed by Chen and Wu [Large interval limit of R\'enyi entropy at high temperature, arXiv:1412.0763], the effective way to read the entropy in the large interval limit is to insert a complete set of state bases of the twist sector at the branch cut.
• Then the calculation transforms into an expansion of four-point functions in the twist sector with respect to $e^{-\frac{2\pi TR}{n}}$.