Maths HEP Lunchtime Seminars: On timelike and spacelike minimal surfaces in AdS_n and the Alday-Maldacena conjecture
27 February 2009 13:00 in CLC407
Motivated by the Alday-Maldacena conjecture, relating gluon scattering amplitudes to minimal surfaces in AdS_5 approaching a lightlike polygon on the boundary, we consider some issues of timelike and spacelike minimal surfaces in generic AdS_n. The discussion uses both the standard differential geometric language ( Gauss, Codazzi and Ricci eqs.) as well as elements of Pohlmeyer reduction for nonlinear sigma models. After the general formulation we restrict ourselves to the subset of flat minimal surfaces. We show that there are no flat spacelike minimal surfaces in AdS_5 beyond those used by Alday-Maldacena for the tetragon case.