Abstract
We establish the large central charge behaviour of the entanglement negativity for a mixed state configuration of a single interval enclosed between two intervals in a holographic $CFT_{1+1}$. To this end we utilize the monodromy technique to elucidate the large central charge limit of a four point twist correlator which characterizes the negativity of the mixed state configuration. Subsequently we analyze the large central charge limit of the six point twist correlator which reduces to the above four point correlator in a specific limit. The results provide a strong consistency check for our recently proposed holographic entanglement negativity conjecture in the $AdS_3/CFT_2$ scenario.
Highlights
Over the last decade significant advances in the understanding of quantum entanglement in the framework of the AdS-CFT correspondence has revealed a remarkable connection with issues of quantum gravity and the structure of space time [1,2,3]
We would like to emphasize that this configuration is relevant to the recently proposed CMS conjecture for the holographic entanglement negativity of bipartite systems described by a CFT1þ1
To this end we have elucidated the large central charge limit of a four point twist correlator characterizing the entanglement negativity of the relevant mixed state
Summary
Over the last decade significant advances in the understanding of quantum entanglement in the framework of the AdS-CFT correspondence has revealed a remarkable connection with issues of quantum gravity and the structure of space time [1,2,3]. On the other hand for the finite temperature mixed state of a CFT1þ1, the dual bulk corresponds to the BTZ black hole In this case the holographic conjecture described by Eq (19) leads to following expression for entanglement negativity: πcl 2β ð25Þ. The above discussions lead to the significant issue of examining the large central charge limit of the four point twist correlator in Eq (12) in order to investigate the consistency of this holographic conjecture In this context, in the subsequent sections, we will utilize the monodromy technique to demonstrate that the universal part of the entanglement negativity given by Eq (23) is dominant in the large central charge limit where as the nonuniversal part of the negativity described by the function gðxÞ in Eqs.
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