A New Covariant Entropy Bound from Cauchy Slice Holography
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Soni, Ronak M Wall, Aron C. |
| author_facet | Soni, Ronak M Wall, Aron C. |
| contents | We begin an investigation of a new holographic covariant entropy bound (HCEB) in gravity. This bound arises from Cauchy slice holography, a recently proposed duality between the bulk gravity theory and a `boundary' theory that lives on Cauchy slices. The HCEB is the logarithm of the maximum number of states of this theory that can pass through a given cut $σ$ of a Cauchy slice $Σ$ ($σ$ is thus a codimension-2 surface in the bulk). We show that the bound depends only on the codimension-2 data on $σ$, and is thus independent of the choice of slice $Σ$. For classical states, the HCEB upper bounds the entanglement between two subregions of the boundary of $Σ$.
We calculate the bound explicitly in pure three-dimensional GR with negative cosmological constant, where the Cauchy slice theory is the $T \overline{T}$-deformation of the dual CFT. We find that the imaginary energy eigenstates in the spectrum of the deformed theory play a crucial role for obtaining a valid bound in Lorentzian signature. Our bound agrees with the area of a surface at certain marginal and extremal surfaces, but differs elsewhere. In particular, it exceeds the area by an arbitrarily large amount for (anti)trapped surfaces, such as those that lie inside a black hole. Finally, we discuss how these results can be used to write down tensor networks corresponding to arbitrary Cauchy slices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A New Covariant Entropy Bound from Cauchy Slice Holography Soni, Ronak M Wall, Aron C. High Energy Physics - Theory General Relativity and Quantum Cosmology We begin an investigation of a new holographic covariant entropy bound (HCEB) in gravity. This bound arises from Cauchy slice holography, a recently proposed duality between the bulk gravity theory and a `boundary' theory that lives on Cauchy slices. The HCEB is the logarithm of the maximum number of states of this theory that can pass through a given cut $σ$ of a Cauchy slice $Σ$ ($σ$ is thus a codimension-2 surface in the bulk). We show that the bound depends only on the codimension-2 data on $σ$, and is thus independent of the choice of slice $Σ$. For classical states, the HCEB upper bounds the entanglement between two subregions of the boundary of $Σ$. We calculate the bound explicitly in pure three-dimensional GR with negative cosmological constant, where the Cauchy slice theory is the $T \overline{T}$-deformation of the dual CFT. We find that the imaginary energy eigenstates in the spectrum of the deformed theory play a crucial role for obtaining a valid bound in Lorentzian signature. Our bound agrees with the area of a surface at certain marginal and extremal surfaces, but differs elsewhere. In particular, it exceeds the area by an arbitrarily large amount for (anti)trapped surfaces, such as those that lie inside a black hole. Finally, we discuss how these results can be used to write down tensor networks corresponding to arbitrary Cauchy slices. |
| title | A New Covariant Entropy Bound from Cauchy Slice Holography |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.16769 |