A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra

TL;DR

This paper introduces a lattice model linked to the $OSp(2S+2|2S)$ supercoset sigma model, focusing on algebraic structures like the Brauer algebra and their role in the model's symmetries.

Contribution

It provides a detailed algebraic analysis of the lattice model's symmetries and bimodule decomposition, connecting lattice structures to conformal field theory insights.

Findings

V^{⊗L} is a nonsemisimple bimodule for $OSp(2S+2|2S)$ and the Brauer algebra.

The lattice model is argued to belong to the same universality class as the supercoset sigma model.

The algebraic structures elucidate the symmetry properties relevant for conformal field theory.

Abstract

We define and study a lattice model which we argue is in the universality class of the $OSp(2S+2|2S)$ supercoset sigma model for a large range of values of the coupling constant $g_\sigma^2$. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain $V^{\otimes L}$ as a bimodule over $OSp(2S+2|2S)$ and its commutant, the Brauer algebra $B_L(2)$. It turns out that $V^{\otimes L}$ is a nonsemisimple module for both $OSp(2S+2|2S)$ and $B_L(2)$. The results are used in the companion paper to elucidate the structure of the (boundary) conformal field theory.