https://doi.org/10.1140/epjc/s10052-017-5292-9
Regular Article - Theoretical Physics
Static elliptic minimal surfaces in 
Institute of Nuclear and Particle Physics, NCSR “Demokritos”, 15310, Aghia Paraskevi, Attiki, Greece
* e-mail: pastras@inp.demokritos.gr
Received:
6
September
2017
Accepted:
8
October
2017
Published online:
23
November
2017
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 , 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 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
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.
© The Author(s), 2017
