Replica trick and string winding

Abstract

We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, both in the open and closed string picture.Comment: 13 pages, 2 figure

A perturbative expansion for entanglement entropy in string theory

“…Because this does not add much to the principal discussion however, and many other technical points had to be introduced, we decided to skip it for the moment. We plan to come back to the classical contributions and their relation with our old work [23] in the future.…”

“…In the second case we would have a two dimensional metric on each sheet as the field to be replicated, and the gauge fixing occurring at the level of the foliated Riemann surface; then each sheet would end up with its own set of moduli and the replicated world sheet becomes a generic higher genus surface. In [23] it was seen that, for the very specific case of one loop open string amplitudes, the mechanism of tadpole cancellation makes the two descriptions equivalent, but for any other topology this is not expected.…”

“…[10] instead considered a specific setting by choosing the closed string theory dual to two dimensional Yang-Mills while [3] pursued the path of a string field theoretic approach. In [23] we instead focused on the pure world sheet problem by considering contributions from winding states and only on a second stage its target space interpretation. Other related papers are [13], [15], [19], [22] and [24].…”

Entanglement, replicas, and Thetas

“…This means that the twist-operator computation, at least in the form currently known, is inadequate to compute the (finite size, finite temperature) Rényi entropy of the free Majorana (Ising)/free Dirac CFT. Subsequent to [12], issues regarding summing over fermion spin structures when computing Rényi entropies have been discussed in different contexts in [14][15][16][17][18].…”

Entanglement in a Maxwell theory coupled to a non-relativistic particle

“…Spatial EE in massive field theories has also been well studied, see for example [15][16][17][18][19][20]. One can also consider the entanglement between other partitions of the Hilbert space that are not spatial ones, as, for example, between right and left moving excitations [21][22][23] or between winding modes [24].…”