Euclidean Wilson loops and minimal area surfaces in lorentzian AdS3

The AdS/CFT correspondence relates Wilson loops in N = 4 SYM theory to minimal area surfaces in AdS(5) x S-5 space. If the Wilson loop is Euclidean and con fined to a plane (t,x) then the dual surface is Euclidean and lives in Lorentzian AdS(3) subset of AdS(5). In this paper we study such minimal area surfaces generalizing previous results obtained in the Euclidean case. Since the surfaces we consider have the topology of a disk, the holonomy of the flat current vanishes which is equivalent to the condition that a certain boundary Schrodinger equation has all its solutions anti-periodic. If the potential for that Schrodinger equation is found then reconstructing the surface and finding the area become simpler. In particular we write a formula for the Area in terms of the Schwarzian derivative of the contour. Finally an in finite parameter family of analytical solutions using Riemann Theta functions is described. In this case, both the area and the shape of the surface are given analytically and used to check the previous results.