New open string solutions inAdS5

Abstract

We describe new solutions for open string moving in AdS 5 and ending in the boundary, namely dual to Wilson loops in N = 4 SYM theory. First we introduce an ansatz for Euclidean curves whose shape contains an arbitrary function. They are BPS and the dual surfaces can be found exactly.After an inversion they become closed Wilson loops whose expectation value is W = exp(− √ λ).After that we consider several Wilson loops for N = 4 SYM in a pp-wave metric and find the dual surfaces in an 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 N = 4 SYM in flat space.

D-brane description of new open string solutions in AdS5

“…On the other hand we also find that the on-shell action vanishes corresponding to the expectation value of the corresponding Wilson line < W >= 1. This is in complete agreement with the result presented in [22].…”

“…Following [20] we consider D5-brane with Euclidean world-volume. Then we shown that the solutions of the equations of motion correspond to the solution found in the first part of the paper [22]. Further, when we evaluate the action on this solution we obtain regularized value of the action that corresponds to the Wilson line in level Π anti-symmetric representation.…”

“…We explicitly found D3 and D5-brane configurations that are analogue of fundamental string solutions given in [22] and that correspond to dual Wilson loop in level Π anti-symmetric and symmetric representations. We mean that this agreement further supports the claim that D3-branes and D5-branes configurations that end on the boundary of AdS 5 correspond to expectation values of some non-local operators in dual N = 4 SYM theory.…”

“…First of all it would be certainly interesting to find D3-brane configurations that correspond to the generalization of the circular Wilson line as in [22]. This is very interesting problem since description of circular Wilson loops in terms of D3-branes is rather non-trivial as was shown in [18].…”

“…In recent interesting paper [22] new open string solutions in AdS 5 were found. Further, it was shown that these string solutions end at the boundary on various Wilson lines.…”