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

TL;DR

This work extends the spin-chain/string correspondence to the non-compact supersymmetric sector SU$(1,1|1)$. By constructing SU$(1,1|1)$ coherent states, the authors obtain a compact, logarithmic effective Hamiltonian that, in the continuum limit, yields a linear sigma model on the supercoset $G/H$ with $G=SU(1,1|1)$ and $H=SU(1|1)\times U(1)$. The resultant action, written in terms of Cartan forms, matches the Green-Schwarz superstring action for fast-spinning configurations on $AdS_5\times S^5$, establishing a precise map between spin-chain coherent states and semiclassical string states. This work generalizes prior compact-case analyses (e.g., SU$(1|2)$) and provides a robust framework for exploring string dynamics in non-compact supersymmetric sectors. The derived dictionary between spin-chain data and string variables offers a bottom-up route to study more general string configurations in $AdS_5\times S^5$.

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.