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Timelike Entanglement Entropy from Rindler Method
For a Lorentzian invariant theory, the entanglement entropy should be a
function of the dependence of domain of the subregion under consideration. More
precisely, it should be a function of the dependence of domain and the
appropriate cut-off. In this paper, we define the concept of cut-off to make it
applicable to timelike regions and assume that the usual entanglement entropy
formula also applies to timelike intervals. Using the Rindler method, the
timelike entanglement entropy can be regarded as the thermal entropy of the CFT
after the Rindler transformation plus a constant with the central
charge of the CFT. The gravitational dual of the timelike entanglement entropy
is finally presented following this method.Comment: 14 pages, 3 figure
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