论文标题
洛伦齐亚·托达·菲尔德理论
Lorentzian Toda field theories
论文作者
论文摘要
我们建议基于洛伦兹晶格定义的根系，为新类TODA现场理论提供几种不同类型的构建原理。类似于基于半简单谎言代数的根系的共形和仿射TODA理论，它们的洛伦兹扩展也出现在保形和庞大的变体中。我们对所提出的理论进行了Parelevé的可合道性测试，通常发现只有一个与能量量张量相对应的整数值。因此，大多数Lorentzian Toda场理论都不可整合，因为其余的共鸣，即半密度案例中W-代数的旋转级是非整数或复杂值的。我们详细分析了几种大型变体的经典质谱。 Lorentzian Toda字段理论可以被视为配备代数框架的可扰动版本的扰动版本。
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.
