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Scanning space-time with patterns of entanglement
- Source :
- Phys. Rev. D 101, 066021 (2020)
- Publication Year :
- 2020
-
Abstract
- In the ${\rm AdS}_3/{\rm CFT}_2$ setup we elucidate how gauge invariant boundary patterns of entanglement of the CFT vacuum are encoded into the bulk via the coefficient dynamics of an $A_{N-3}$, $N\geq 4$ cluster algebra. In the static case this dynamics of encoding manifests itself in kinematic space, which is a copy of de Sitter space ${\rm dS}_2$, in a particularly instructive manner. For a choice of partition of the boundary into $N$ regions the patterns of entanglement, associated with conditional mutual informations of overlapping regions, are related to triangulations of geodesic $N$-gons. Such triangulations are then mapped to causal patterns in kinematic space. For a fixed $N$ the space of all causal patterns is related to the associahedron ${\mathcal K}^{N-3}$ an object well-known from previous studies on scattering amplitudes. On this space of causal patterns cluster dynamics acts by a recursion provided by a Zamolodchikov's $Y$-system of type $(A_{N-3},A_1)$. We observe that the space of causal patterns is equipped with a partial order, and is isomorphic to the Tamari lattice. The mutation of causal patterns can be encapsulated by a walk of $N-3$ particles interacting in a peculiar manner in the past light cone of a point of ${\rm dS}_2$.<br />Comment: 18 pages, 15 figures
- Subjects :
- High Energy Physics - Theory
Mathematical Physics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. D 101, 066021 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.2001.07923
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.101.066021