双曲陪集模型中的Sugawara型约束
Sugawara-type constraints in hyperbolic coset models
摘要：
在无限维双曲陪集空间，特别是E10/K（E10）上的超引力模型和测地线模型之间的严格对应中，约束起着核心作用。我们提出了一个Sugawara型结构的E10 Noether收费，这些限制无限扩展到双曲代数，在arXiv：0709.2691中得到的截断表达式，只涉及到200多个发电机。我们的扩展约束相关联的一组无限的根都是虚构的，实际上填补了封闭的过去光锥的洛伦兹根晶格。这个结构利用了E10 Weyl群，以及E10模型包含D=11超引力和D=10 IIB超引力的事实。我们的扩展约束似乎以一种非凡的方式统一了这两个理论的不同规范约束。这一建设也可能揭示新的光的问题上的“开放约束代数”在传统的规范方法的重力。
英文摘要：
In the conjectured correspondence between supergravity and geodesic models on infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the constraints play a central role. We present a Sugawara-type construction in terms of the E10 Noether charges that extends these constraints infinitely into the hyperbolic algebra, in contrast to the truncated expressions obtained in arXiv:0709.2691 that involved only finitely many generators. Our extended constraints are associated to an infinite set of roots which are all imaginary, and in fact fill the closed past light-cone of the Lorentzian root lattice. The construction makes crucial use of the E10 Weyl group and of the fact that the E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our extended constraints appear to unite in a remarkable manner the different canonical constraints of these two theories. This construction may also shed new light on the issue of `open constraint algebras' in traditional canonical approaches to gravity.
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