Renyi entropies of free bosons on the torus and holography

Datta, Shouvik and David, Justin R (2014) Renyi entropies of free bosons on the torus and holography. In: JOURNAL OF HIGH ENERGY PHYSICS (4).

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Abstract

We analytically evaluate the Renyi entropies for the two dimensional free boson CFT. The CFT is considered to be compactified on a circle and at finite temperature. The Renyi entropies S-n are evaluated for a single interval using the two point function of bosonic twist fields on a torus. For the case of the compact boson, the sum over the classical saddle points results in the Riemann-Siegel theta function associated with the A(n-1) lattice. We then study the Renyi entropies in the decompactification regime. We show that in the limit when the size of the interval becomes the size of the spatial circle, the entanglement entropy reduces to the thermal entropy of free bosons on a circle. We then set up a systematic high temperature expansion of the Renyi entropies and evaluate the finite size corrections for free bosons. Finally we compare these finite size corrections both for the free boson CFT and the free fermion CFT with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces as its boundary. One-loop corrections in these geometries are entirely determined by quantum numbers of the excitations present in the bulk. This implies that the leading finite size corrections contributions from one-loop determinants of the Chern-Simons gauge field and the Dirac field in the dual geometry should reproduce that of the free boson and the free fermion CFT respectively. By evaluating these corrections both in the bulk and in the CFT explicitly we show that this expectation is indeed true.

Item Type:	Journal Article
Publication:	JOURNAL OF HIGH ENERGY PHYSICS
Publisher:	SPRINGER
Additional Information:	Copyright for this article belongs to the SPRINGER, USA
Keywords:	AdS-CFT Correspondence; Conformal Field Models in String Theory
Department/Centre:	Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited:	19 May 2014 05:25
Last Modified:	19 May 2014 05:25
URI:	http://eprints.iisc.ac.in/id/eprint/49095

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