arXiv 1402.73062014-02-28hep-thmath-phmath.MPmath.QAquant-ph

非几何弦论中的非结合几何和扭曲变形

Nonassociative geometry and twist deformations in non-geometric string theory

Dionysios Mylonas, Peter Schupp, Richard J. Szabo

备注：: 28 pages; Based on lectures given at ICMP 2013, 21-26 October, 2013, Londrina, Brazil; to appear in Proceedings of Science

摘要：

我们在弦论的非几何流紧化中描述了闭弦所探测的几何的非结合变形。我们表明，这些非几何背景可以通过开膜的边界在目标空间紧化的相空间中传播，配备了扭曲的泊松结构的动态geometrised。有效膜靶空间由动量空间中被交换几何体扭曲的靶空间上的标准Courant代数体确定。膜西格玛模型的量化导致适当的量化的非几何背景，我们涉及到Kontsevich的形式主义的全球变形量化，构建一个noncommutative nonassociative星产品相空间。我们构造Seiberg-Witten型映射之间的关联和非关联的背景，并显示它们如何可能实现非关联变形的重力。我们还解释了这种方法是如何与量子化的某些李2-代数规范相关的扭曲的柯朗代数体，和cochain扭曲量子化使用合适的拟Hopf代数的对称性在相空间描述的R-空间，它构造了一个Drinfel的扭曲与非平凡的3-cocycle。我们说明并应用我们的形式主义，提出了一个一致的非结合量子力学的相空间制定。

英文摘要：

We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure. The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space. Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras canonically associated to the twisted Courant algebroid, and cochain twist quantization using suitable quasi-Hopf algebras of symmetries in the phase space description of R-space which constructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and apply our formalism to present a consistent phase space formulation of nonassociative quantum mechanics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文