Generalized sine-Gordon models and quantum braided groups

TL;DR

This paper explores the quantization of generalized sine-Gordon models, establishing that affine quantum braided groups provide the natural framework for their quantum lattice integrable structures.

Contribution

It identifies the quantized function algebras for these models as quadratic algebras of Freidel-Maillet type, linking classical limits to lattice Poisson algebras and proposing affine quantum braided groups as the key framework.

Findings

Quantized function algebras are quadratic Freidel-Maillet type.

Classical limits reproduce lattice Poisson algebra.

Affine quantum braided groups are suitable for quantum integrable models.

Abstract

We determine the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson algebra recently obtained for these models defined by a gauged Wess-Zumino-Witten action plus an integrable potential. More specifically, we argue based on these examples that the natural framework for constructing quantum lattice integrable versions of generalized sine-Gordon models is that of affine quantum braided groups.