A new look at the entanglement entropy of a single interval in a 2d CFT

Abstract

In this note, I revisit the problem of computing the entanglement entropy of a single interval in the ground state of a 2d CFT. I write the leading-order result in three different ways: once by doing the replica trick with the $n$-replicated cylinder partition function computed in the ``closed string channel"; once by computing the $n$-replicated cylinder partition function in the ``open string channel", where the entanglement entropy can be related to the density of states in a boundary CFT defined on the interval; and for holographic CFTs, once as the log of a Plancherel measure for a certain noncompact quantum group. I comment on the implications for what the Ryu-Takayanagi area term might be counting in holographic CFTs.

4 pages. v3: typos fixed

References in corpus (5)

• The entropy of Hawking radiation
• Physics at the entangling surface
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Lectures on entanglement entropy in field theory and holography
• Entanglement entropy in Jackiw-Teitelboim gravity with matter

Cited by in corpus (1)

• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra