Monodromy methods for torus conformal blocks and entanglement entropy at large central charge

TL;DR

This paper develops monodromy methods to compute entanglement entropy in 2D conformal field theories at large central charge, revealing universal behaviors consistent with holographic predictions.

Contribution

It introduces a generalized monodromy approach for torus conformal blocks and applies it to entanglement entropy calculations, extending previous methods.

Findings

Vacuum exchange dominates entanglement entropy in large central charge CFTs

Results agree with holographic RT formula predictions

Identifies regimes where replica partition function matches local twist operator correlations

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.