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

TL;DR

This paper derives the low-energy effective actions for spinning strings in AdS(3) x S(3) x M(4), demonstrating their classical integrability through Lax connections, with different models depending on the choice of M(4).

Contribution

It presents the explicit form of the low-energy effective actions for these strings and proves their classical integrability via Lax connections.

Findings

Effective actions are composed of coupled sigma models and fermions.

Models are shown to be classically integrable.

Different M(4) choices lead to distinct integrable models.

Abstract

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.