From algebraic curve to minimal surface and back

Abstract

We derive the Lax operator for a very large family of classical minimal surface solutions in $Ad{S}_3$ describing Wilson loops in $\mathcal{N}=4$ SYM theory. These solutions, constructed by Ishizeki, Kruczenski and Ziama, are associated with a hyperellictic surface of odd genus. We verify that the algebraic curve derived from the Lax operator is indeed none-other than this hyperelliptic surface.

21 pages

References in corpus (1)

• Wilson loops and minimal area surfaces in hyperbolic space

Cited by in corpus (1)

• Dual conformal transformations of smooth holographic Wilson loops