Lorentzian Toda field theories
arXiv:2005.13582 · doi:10.1142/S0129055X21500173
Abstract
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 semisimple cases, are either non integer or complex valued. We analyse 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.
arXiv comment22 pages, 4 figures
References in corpus (12)
- E10 and a "small tension expansion" of M Theory
- Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
- Quantum Solitons in Affine Toda Field Theories
- A class of Lorentzian Kac-Moody algebras
- Hirota's Solitons in the Affine and the Conformal Affine Toda Models
- Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
- On the universal Representation of the Scattering Matrix of Affine Toda Field Theory
- Vertex Operators and Soliton Time Delays in Affine Toda Field Theory
- The Painleve Property, W Algebras and Toda Field Theories associated with Hyperbolic Kac-Moody Algebras
- Affine Toda field theories related to Coxeter groups of non-crystallographic type
- The Principal SO(1,2) Subalgebra of a Hyperbolic Kac Moody Algebra
- N-Extended Lorentzian Kac-Moody algebras