Static elliptic minimal surfaces in [Formula omitted]

The Ryu-Takayanagi conjecture connects the entanglement entropy in the boundary CFT to the area of open co-dimension two minimal surfaces in the bulk. Especially in [Formula omitted], the latter are two-dimensional surfaces, and, thus, solutions of a Euclidean non-linear sigma model on a symmetric t...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2017-11, Vol.77 (11)
Main Author: Pastras, Georgios
Format: Article
Language:English
Online Access:Get full text
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Summary:The Ryu-Takayanagi conjecture connects the entanglement entropy in the boundary CFT to the area of open co-dimension two minimal surfaces in the bulk. Especially in [Formula omitted], the latter are two-dimensional surfaces, and, thus, solutions of a Euclidean non-linear sigma model on a symmetric target space that can be reduced to an integrable system via Pohlmeyer reduction. In this work, we construct static minimal surfaces in [Formula omitted] that correspond to elliptic solutions of the reduced system, namely the cosh-Gordon equation, via the inversion of Pohlmeyer reduction. The constructed minimal surfaces comprise a two-parameter family of surfaces that include helicoids and catenoids in H [Formula omitted] as special limits. Minimal surfaces that correspond to identical boundary conditions are discovered within the constructed family of surfaces and the relevant geometric phase transitions are studied.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-017-5292-9