Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)

TL;DR

This paper establishes an equivalence between a specific spin-chain model with PSU(2|2)xU(1)^3 symmetry and a non-linear sigma-model on a coset space, highlighting the role of the supergroup D(2,1;gamma) in their symmetry structure.

Contribution

It demonstrates the correspondence between the spin-chain and sigma-model, identifying the spin-variable as the Killing scalar and linking their integrability properties.

Findings

Spin-chain with PSU(2|2)xU(1)^3 symmetry is equivalent to a specific non-linear sigma-model.

Correlation functions of both theories can share the same integrability.

The symmetry arises from a reduction of the supergroup D(2,1;gamma).

Abstract

We propose that the spin-chain with the PSU(2|2)xU(1)^3 symmetry is equivalent to the non-linear sigma-model on PSU(2|2)xU(1)^3/{HxU(1)} with a certain subgroup. To this end we show that the spin-variable of the former theory is identified as the Killing scalar of the latter and their correlation functions can have the same integrability. It is crucial to think that the respective theory gets the PSU(2|2)xU(1)^3 symmetry by a symmetry reduction the exceptional supergroup D(2,1;gamma), rather than by an extension of PSU(2|2).