Target Space Entanglement Entropy

Mazenc, Edward A.; Ranard, Daniel

doi:10.48550/arxiv.1910.07449

Cited by 18 publications

(38 citation statements)

References 21 publications

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“…It would be interesting to see if our result can be understood in terms of Susskind and Uglum's prescription to compute string theory partition function on off-shell backgrounds [3]. Another intriguing proposal in this regard is [44] which introduces the idea of target space entanglement entropy which seems a natural notion to study entanglement entropy in string theory from a worldsheet point of view.…”

Section: Worldsheet Perspectivementioning

confidence: 93%

Entanglement Entropy in Closed String Theory

Naseer¹

2020

Preprint

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In local quantum field theory on a background spacetime, the entanglement entropy of a region is divergent due to the arbitrary short-wavelength correlations near the boundary of the region. Quantum gravitational fluctuations are expected to cut off the entropy of the ultraviolet modes. We study the entanglement entropy in closed string theory using the framework of string field theory. In particular, we compute the one-loop Renyi partition functions by considering the theory on a simple branched cover of the configuration space of closed strings. The shortwavelength modes are cut off at the string scale and the one-loop entanglement entropy is ultraviolet-finite. A non-canonical kinetic term, required to produce the correct one-loop vacuum amplitude, plays a key role.

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Section: Worldsheet Perspectivementioning

confidence: 93%

Entanglement Entropy in Closed String Theory

Naseer¹

2020

Preprint

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“…This is very important toward the understanding of the interior of the black hole, where a simple geometric picture discussed in this paper may not be applicable. Recently there are several attempts to use the entanglement between color degrees of freedom for this purpose [40,41,42,43,44,45,46]. It would be useful to study the meanings of these proposals, or to make a better proposal, based on the geometric picture discussed in this paper.…”

Section: Future Directionsmentioning

confidence: 99%

Bulk geometry in gauge/gravity duality and color degrees of freedom

Hanada

2021

Preprint

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U(N ) supersymmetric Yang-Mills theory naturally appears as the low-energy effective theory of a system of N D-branes and open strings between them. Transverse spatial directions emerge from scalar fields, which are N × N matrices with color indices; roughly speaking, the eigenvalues are the locations of D-branes. In the past, it was argued that this simple 'emergent space' picture cannot be used in the context of gauge/gravity duality, because the ground-state wave function delocalizes at large N , leading to a conflict with the locality in the bulk geometry. In this paper we show that this conventional wisdom is not correct: the ground-state wave function does not delocalize, and there is no conflict with the locality of the bulk geometry. This conclusion is obtained by clarifying the meaning of the 'diagonalization of a matrix' in Yang-Mills theory, which is not as obvious as one might think. This observation opens up the prospect of characterizing the bulk geometry via the color degrees of freedom in Yang-Mills theory, all the way down to the center of the bulk.

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“…x < x o and x > x o . In the original matrix quantum mechanics this is a 'target space entanglement' [35] of the eigenvalues. In Appendix B we show how to map this entanglement onto a 'base space entanglement' of the collective field n(x).…”

Section: Boundary Entanglementmentioning

confidence: 99%

Entanglement in the Quantum Hall Matrix Model

Frenkel,

Hartnoll

2021

Preprint

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Characterizing the entanglement of matrix degrees of freedom is essential for understanding the holographic emergence of spacetime. The Quantum Hall Matrix Model is a gauged U (N ) matrix quantum mechanics with two matrices whose ground state is known exactly and describes an emergent spatial disk with incompressible bulk dynamics. We define and compute an entanglement entropy in the ground state associated to a cut through the disk. There are two contributions. A collective field describing the eigenvalues of one of the matrices gives a gauge-invariant chiral boundary mode leading to an expected logarithmic entanglement entropy. Further, the cut through the bulk splits certain 'off-diagonal' matrix elements that must be duplicated and associated to both sides of the cut. Sewing these duplicated modes together in a gauge-invariant way leads to a bulk 'area law' contribution to the entanglement entropy. All of these entropies are regularized by finite N .

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Target Space Entanglement Entropy

Cited by 18 publications

References 21 publications

Entanglement Entropy in Closed String Theory

Entanglement Entropy in Closed String Theory

Bulk geometry in gauge/gravity duality and color degrees of freedom

Entanglement in the Quantum Hall Matrix Model

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