The low energy limit of the AdS(3) x S(3) x M(4) spinning string

Understand

We derive the low-energy effective action for the spinning (GKP) string in AdS(3) x S(3) x M(4) where M(4) = S(3) x S(1) or T(4).

• In the first case the action consists of two O(4) non-linear sigma models which are coupled through their interaction with four massless Majorana fermions (plus one free decoupled scalar).
• While in the second case it consists of one O(4) sigma model coupled to four Majorana fermions together with four free scalars from the T(4).
• We show that these models are classically integrable by constructing their Lax connections.