New open string solutions inAdS5

Abstract

We describe new solutions for open string moving in ${\mathrm{AdS}}_5$ and ending in the boundary, namely, dual to Wilson loops in $\mathcal{N}=4$ SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are Bogomol’nyi-Prasad-Sommerfield monopoles (BPS) and the dual surfaces can be found exactly. After an inversion they become closed Wilson loops whose expectation value is $W=\exp (-\sqrt{\lambda })$. After that we consider several Wilson loops for $\mathcal{N}=4$ SYM in a $pp$-wave metric and find the dual surfaces in an ${\mathrm{AdS}}_5$ $pp$-wave background. Using the fact that the $pp$-wave is conformally flat, we apply a conformal transformation to obtain novel surfaces describing strings moving in AdS space in Poincare coordinates and dual to Wilson loops for $\mathcal{N}=4$ SYM in flat space.