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

TL;DR

The authors derive the low-energy effective action for the GKP spinning string in $AdS_3\times S^3\times M_4$, with $M_4=S^3\times S^1$ or $T^4$, revealing two $O(4)$ sigma models coupled to four Majorana fermions (plus a decoupled scalar) for the $S^3\times S^1$ case, or a single $O(4)$ sigma model with four fermions and four free scalars for the $T^4$ case. By integrating out the massive boson and fixing kappa symmetry appropriately, the quartic fermion terms cancel, yielding a clean low-energy theory with manifest integrability evidenced by a Lax pair. The classical integrability is established via two decoupled Lax components corresponding to each $S^3$ factor, whose flatness follows on-shell. This work clarifies the massless sector dynamics in this AdS$_3$/CFT$_2$ setting and paves the way for future quantum analyses, including Bethe Ansatz and S-matrix considerations for the low-energy theory, as well as explorations with mixed RR/NSNS flux.

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.