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

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.

28 pages, 5 figures; v2: added references; v3: published version; v4: fixed typos

References in corpus (14)

• Entanglement negativity in quantum field theory
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Finite temperature entanglement negativity in conformal field theory
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Entwinement and the emergence of spacetime
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• Bose-Fermi duality and entanglement entropies
• Single Interval Rényi Entropy At Low Temperature
• Entwinement in discretely gauged theories
• Semi-classical Virasoro blocks: proof of exponentiation
• Holographic duals of large-c torus conformal blocks
• Universal relation between thermal entropy and entanglement entropy in CFT
• Rényi Entropy of Free Compact Boson on Torus

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• Generalized monodromy method in gauge/gravity duality
• Bulk quantum corrections to entwinement