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arXiv · 0801.0430

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

Constantin Candu·Hubert Saleur
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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 $g_σ^2$. 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.

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Constantin Candu, Hubert Saleur. 2008-01-02. A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra. https://doi.org/10.1016/j.nuclphysb.2008.09.034

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