On affine Toda field theories related to \({\bf D}_r\) algebras and their real Hamiltonian forms

The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series \({\bf D}_r\). We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of \(\mathfra...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Gerdjikov, Vladimir S, Grahovski, Georgi G
Format: Article
Language:English
Subjects:
Automorphisms
Lie groups
Online Access:Get full text
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Summary:The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series \({\bf D}_r\). We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of \(\mathfrak{g}\). This is illustrated on the examples \({\bf D}_{r+1}^{(1)} \to {\bf B}_r^{(1)}\) and \({\bf D}_4^{(1)} \to {\bf G}_2^{(1)}\) using external automorphisms of the corresponding extended Dynkin diagrams.
ISSN:2331-8422
DOI:10.48550/arxiv.2401.18027