Quantum sl_n Toda field theories
L.Bonora, V.Bonservizi
TL;DR
This paper develops a quantum lattice formulation of $sl_n$ Toda field theories, deriving the quantum exchange algebra and relating it to known quantum $R$ matrices, with explicit analysis for $sl_3$.
Contribution
It introduces a quantum lattice approach for $sl_n$ Toda theories and clarifies the connection between different quantum $R$ matrices, including for the second fundamental representation.
Findings
Derived the quantum exchange algebra in the Bloch wave basis.
Extended analysis to the second fundamental representation for $sl_3$.
Clarified the relation between Jimbo-Rosso's and the Bloch wave basis quantum $R$ matrices.
Abstract
We quantize Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the case of the defining representation. In the case we extend the analysis also to the second fundamental representation. We clarify, in particular, the relation of Jimbo and Rosso's quantum matrix with the quantum matrix in the Bloch wave basis.
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