From eta-deformed Neumann-Rosochatius to Geodesics on the Sausage

by Daniel Medina-Rincon (Hamburg University/Nordita), Martin Heinze (Hamburg University/Nordita)

Monday 3 Oct 2016, 13:15 → 14:15 Europe/Stockholm

132:028

Recently, the superstring on AdS_5 × S^5 has been generalized by its so-called eta-deformation and we present work on two string solutions in this integrable background. First, we consider spinning solutions leading to a generalization of the Neumann-Rosochatius system. Especially, from the Lax matrix we deduce a sufficient number of integrals of motion, showing its Liouville integrability. We then restrict to geodesics on eta-deformed S^2 alias the Fateev sausage model. Here, we find three integrals of motion forming an sl(2) algebra, showing maximal superintegrability of the system. This motivates to construct a canonical map to an auxiliary S^2, which solves the geodesic problem while leaving some open questions.