Superstring sigma models from spin chains: the SU(1,1|1) case

TL;DR

This paper derives a sigma model from an SU(1,1|1) spin chain, linking it to string dynamics on supercosets and demonstrating agreement with the Green-Schwarz string action in AdS_5 x S^5.

Contribution

It introduces a coherent state representation for the non-compact supersymmetric spin chain and connects the resulting sigma model to string theory on supercosets.

Findings

Derived the coherent state representation of the SU(1,1|1) spin chain.

Established the continuous limit leading to a string sigma model.

Showed the sigma model matches the Green-Schwarz string action on AdS_5 x S^5.

Abstract

We derive the coherent state representation of the integrable spin chain Hamiltonian with non-compact supersymmetry group G=SU(1,1|1). By passing to the continuous limit, we find a spin chain sigma model describing a string moving on the supercoset G/H, H being the stabilizer group. The action is written in a manifestly G-invariant form in terms of the Cartan forms and the string coordinates in the supercoset. The spin chain sigma model is shown to agree with that following from the Green-Schwarz action describing two-charged string spinning on AdS_5 x S^5.