Abstract
We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. Moreover, we determine in which regime the replica partition function agrees with a correlation function of local twist operators on the torus.
Highlights
In the semiclassical large central charge limit and at zero temperature, the entanglement entropy again becomes universal for a large class of conformal field theories
We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick
We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula
Summary
This section contains an overview over the monodromy methods used in this publication. We start with a review of the standard monodromy method for conformal blocks on the plane, turn to the case of conformal blocks on the torus and explain how to derive a monodromy method for zero-point blocks of the partition function on the replica surface relevant to the computation of entanglement entropy on the torus
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