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Lorentzian Toda field theories

Fring, A. ORCID: 0000-0002-7896-7161 & Whittington, S. (2021). Lorentzian Toda field theories. Reviews in Mathematical Physics, 33(06), article number 2150017. doi: 10.1142/s0129055x21500173


We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple Lie algebras, also their Lorentzian extensions come about in conformal and massive variants. We carry out the Painlevé integrability test for the proposed theories, finding in general only one integer valued resonance corresponding to the energy-momentum tensor. Thus most of the Lorentzian Toda field theories are not integrable, as the remaining resonances, that grade the spins of the W-algebras in the semi-simple cases, are either non-integer or complex valued. We analyze in detail the classical mass spectra of several massive variants. Lorentzian Toda field theories may be viewed as perturbed versions of integrable theories equipped with an algebraic framework.

Publication Type: Article
Additional Information: Electronic version of an article published as Fring, A. and Whittington, S. (2021). Lorentzian Toda field theories. Reviews in Mathematical Physics, 33(6), 2150017, © World Scientific Publishing Company,
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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