Static Elliptic Minimal Surfaces in AdS(4)

TL;DR

This paper constructs a family of static elliptic minimal surfaces in AdS(4) by inverting Pohlmeyer reduction, revealing new solutions including helicoids and catenoids, and analyzing their phase transitions.

Contribution

It introduces a novel method to invert Pohlmeyer reduction for constructing explicit minimal surfaces in AdS(4), expanding the known solution space.

Findings

Includes a two-parameter family of minimal surfaces

Identifies geometric phase transitions between solutions

Connects minimal surfaces to elliptic solutions of the cosh-Gordon equation

Abstract

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 AdS(4), 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 invert Pohlmeyer reduction to construct static minimal surfaces in AdS(4) that correspond to elliptic solutions of the reduced system, namely the cosh-Gordon equation. The constructed minimal surfaces comprise a two-parameter family of surfaces that include helicoids and catenoids in H(3) 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.