Sigma model from SU(1,1|2) spin chain

TL;DR

This paper derives a sigma model from an SU(1,1|2) supersymmetric spin chain, connecting integrable models to string theory on AdS5 x S5, and explicitly constructs the coherent state representation and the continuous limit.

Contribution

It provides the explicit coherent state representation of the SU(1,1|2) spin chain Hamiltonian and derives the corresponding bosonic and supercoset sigma models.

Findings

The bosonic sigma model is a sum of SU(2) and SL(2) models.

The full supercoset sigma model is explicitly constructed.

Connection established between spin chain dynamics and string theory on AdS5 x S5.

Abstract

We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group $SU(1,1|2)$. By the use of a projected Hamiltonian onto bosonic states, we give explicitly the action of the Hamiltonian on $SU(2)\times SL(2)$ coherent states. Passing to the continuous limit, we find that the corresponding bosonic sigma model is the sum of the known SU(2) and SL(2) ones, and thus it gives a string spinning fast on $S^1_{\phi_1}\times S^1_{\phi_1}\times S^1_{\phi_2}$ in $\rm{AdS}_5 \times S^5$. The full sigma model on the supercoset $SU(1,1|2)/SU(1|1)^2$ is given.