Modular invariance and entanglement entropy

Lokhande, Sagar F.; Mukhi, Sunil

doi:10.48550/arxiv.1504.01921

Cited by 2 publications

(6 citation statements)

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“…In that case the question is whether the sum over spin structures has to be done on each sheet before or after the replica. The two procedures lead to different results, see for example [6,13,18,19], unlike what happens in the present case. 5 As ρ A " ρ, we suppress from now on the somewhat misleading label A, which may induce to believe we are computing entanglement entropy, when in fact we are computing the usual entropy.…”

Section: The Replica Trick On the World-sheetcontrasting

confidence: 73%

“…However, in order to do this computation, some non-trivial issues with the replica trick on the cylinder need to be sorted out first. These include: possible boundary contributions [21]; the fact that string theory is conformal only locally, so that the usual CFT computations should be adapted somehow; 7 the topological structure of the world-sheet that may create problems in defining non-topological entangling regions as, for example, a region that does not extend from one boundary to the other; 8 the still unresolved issue on how to sum over spin structures [13,19]. This last problem, in particular, is quite relevant, as computations on a torus have shown that modular invariance is preserved only if appropriate spin structures are chosen.…”

Section: Discussionmentioning

confidence: 99%

“…This last problem, in particular, is quite relevant, as computations on a torus have shown that modular invariance is preserved only if appropriate spin structures are chosen. More specifically, one has to sum over each sheet and then glue sheets together in the limit of a small entangling region, whereas for a large entangling region one has to select the same spin structure for each sheet first and then sum over structures [19]. These two procedures were inspired by imposing (2).…”

Section: Discussionmentioning

confidence: 99%

“…restricting one of the two domains of integration to a vanishing interval O γ centered around the value of γ of the other integral: trpρ q q " lim Oγ Ñ0 ş dγ ş Oγ dγ 1 xγ|ρ q |γ 1 y. Evaluating the delta functions before the limiting process gets rid of factors of δp0q that would otherwise appear in (19).…”

Section: Closed String Picturementioning

confidence: 99%

“…We can then repeat the procedure of the previous section. The only difference is that the weights in (19) will be replaced by the ones in (22).…”

Section: Closed String Picturementioning

confidence: 99%

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Replica trick and string winding

Prudenziati

Trancanelli

2017

Phys. Rev. D

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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

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Section: The Replica Trick On the World-sheetcontrasting

confidence: 73%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Closed String Picturementioning

confidence: 99%

“…We can then repeat the procedure of the previous section. The only difference is that the weights in (19) will be replaced by the ones in (22).…”

Section: Closed String Picturementioning

confidence: 99%

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Replica trick and string winding

Prudenziati

Trancanelli

2017

Phys. Rev. D

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Holographic calculation for large interval Rényi entropy at high temperature

Chen

2015

Phys. Rev. D

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In this paper, we study the holographic Rényi entropy of a large interval on a circle at high temperature for the two-dimensional CFT dual to pure AdS 3 gravity. In the field theory, the Rényi entropy is encoded in the CFT partition function on n-sheeted torus connected with each other by a large branch cut. As proposed in [7], the effective way to read the entropy in the large interval limit is to insert a complete set of state bases of the twist sector at the branch cut. Then the calculation transforms into an expansion of four-point functions in the twist sector with respect to e − 2πT R n . By using the operator product expansion of the twist operators at the branch points, we read the first few terms of the Rényi entropy, including the leading and next-to-leading contributions in the large central charge limit. Moreover, we show that the leading contribution is actually captured by the twist vacuum module. In this case by the Ward identity the four-point functions can be derived from the correlation function of four twist operators, which is related to double interval entanglement entropy. Holographically, we apply the recipe in [20] and [26] to compute the classical Rényi entropy and its 1-loop quantum correction, after imposing a new set of monodromy conditions. The holographic classical result matches exactly with the leading contribution in the field theory up to e −4πT R and l 6 , while the holographical 1-loop contribution is in exact agreement with next-to-leading results in field theory up to e − 6πT R n and l 4 as well. *

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Modular invariance and entanglement entropy

Cited by 2 publications

References 0 publications

Replica trick and string winding

Replica trick and string winding

Holographic calculation for large interval Rényi entropy at high temperature

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