Topological string entanglement

Journal Article · Thu Oct 24 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep10(2019)239· OSTI ID:1659666

Hubeny, Veronika E. ^[1]; Pius, Roji ^[1]; Rangamani, Mukund ^[1]

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1. Univ. of California, Davis, CA (United States)

We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom is encoded in string theory (beyond the oft discussed classical gravity limit). Concretely, we realize the Chern-Simons theory as the worldvolume dynamics of topological D-branes in the topological A-model string theory on a Calabi-Yau target. Via the open/closed topological string duality one can map this theory onto a pure closed topological A-model string on a different target space, one which is related to the original Calabi-Yau geometry by a geometric/conifold transition. We demonstrate how to uplift the replica construction of Chern-Simons theory directly onto the closed string and show that it provides a meaningful definition of reduced density matrices in topological string theory. Furthermore, we argue that the replica construction commutes with the geometric transition, thereby providing an explicit closed string dual for computing reduced states, and Rényi and von Neumann entropies thereof. While most of our analysis is carried out for Chern-Simons on $$\hbox{S}^3$$, the emergent picture is rather general. Specifically, we argue that quantum entanglement on the open string side is mapped onto quantum entanglement on the closed string side and briefly comment on the implications of our result for physical holographic theories where entanglement has been argued to be crucial ingredient for the emergence of classical geometry.

• Research Organization: Univ. of California, Davis, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019480; NSF PHY17-48958
• OSTI ID: 1659666
• Journal Information: Journal of High Energy Physics (Online), Vol. 2019, Issue 10; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Chern-Simons Theories
Gauge-gravity correspondence
Topological Strings