Dressed Minimal Surfaces in AdS$_4$

TL;DR

This paper explores how dressing transformations can generate new minimal surfaces in AdS4 from known solutions, revealing connections to sigma models and producing novel elliptic minimal surfaces.

Contribution

It introduces a method to generate new minimal surfaces in AdS4 via dressing transformations and relates them to solutions of the Euclidean sigma model in dS3.

Findings

A single dressing transformation relates minimal surfaces to sigma model solutions.

Derived an expression for the area element of dressed surfaces.

Constructed new elliptic minimal surfaces using the formalism.

Abstract

We apply an arbitrary number of dressing transformations to a static minimal surface in AdS(4). Interestingly, a single dressing transformation, with the simplest dressing factor, interrelates the latter to solutions of the Euclidean non linear sigma model in dS(3). We present an expression for the area element of the dressed minimal surface in terms of that of the initial one and comment on the boundary region of the dressed surface. Finally, we apply the above formalism to the elliptic minimal surfaces and obtain new ones.