Horizon molecules in causal set theory

Barton, Christopher; Counsell, Andrew; Dowker, Fay; Gould, Dewi S. W.; Taylor, Gwylim; Jubb, Ian

doi:10.1103/physrevd.100.126008

Cited by 10 publications

(20 citation statements)

References 14 publications

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“…As a final remark, one might also be able to make an interesting connection between our findings and the horizon molecules in [51]; there may be a relation between horizon molecules being links and the entropy up to first order being fully described by two-point functions.…”

Section: Jhep11(2020)114mentioning

confidence: 61%

Towards spacetime entanglement entropy for interacting theories

Chen

Hackl

Kunjwal

et al. 2020

J. High Energ. Phys.

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Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin’s entropy to non-Gaussian theories where Wick’s theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.

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Section: Jhep11(2020)114mentioning

confidence: 61%

Towards spacetime entanglement entropy for interacting theories

Chen

Hackl

Kunjwal

et al. 2020

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…It is worth noting the difference between our analysis and [7] in the spacelike case. The case thereby discussed sees the volumes V and V + tend to the point y in the continuum limit and the integrand of…”

Section: Folded Null Planesmentioning

confidence: 73%

“…We therefore need a patch to fix the horizon molecule proposal if possible. One can naively restore the area-law claimed in [7], by somehow deforming away the null segment in the hypersurface simaltaneously while taking the continuum limit. For instance, we can set…”

Section: Discussionmentioning

confidence: 99%

“…Defining now the expectation value of the number of horizon n-molecules as in [7], and calling p the element p − , one gets to the following identity…”

Section: Horizon Molecule Counting With Null Hypersurfacesmentioning

confidence: 99%

“…Admittedly, horizon molecule can only be a coarse-grained notion of entropy, but it might offer a hint to a deeper understanding of gravitational entropy in the context of causal set theory or generally other discretized theories. See more motivations for studying horizon molecules in [5,6,7,4]. There is another more fine-grained program that studied entropy for quantum fields defined on a causal set by studying correlation functions between spacetime regions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the horizon entropy of a causal set

Machet,

Wang

2020

Preprint

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We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.

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On Horizon Molecules and Entropy in Causal Sets

Dou

2023

Handbook of Quantum Gravity

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Horizon molecules in causal set theory

Cited by 10 publications

References 14 publications

Towards spacetime entanglement entropy for interacting theories

Towards spacetime entanglement entropy for interacting theories

On the horizon entropy of a causal set

On Horizon Molecules and Entropy in Causal Sets

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