几乎Kahler变量下爱因斯坦引力A模型复化的膜和量子化
Branes and Quantization for an A-Model Complexification of Einstein Gravity in Almost Kahler Variables
摘要：
广义相对论理论在几乎所有的卡勒变量中被等价地重新定义：辛形式和正则辛联络（由仅由度量系数及其导数构成的张量从列维-奇维塔联络扭曲而来）。基本的几何和物理对象是唯一确定的度量相容形式的（伪）黎曼度量的流形上启用必要类型的非完整2+2分布。这样的非完整辛变量允许我们用时空流形上几乎复结构的A模型复化来表述量子化爱因斯坦引力的问题，推广了古柯夫-威滕方法，参见arXiv：0809.0305。量子化的复杂化模型，我们推导出一个希尔伯特空间作为一个空间的弦与两个A-膜的爱因斯坦引力理论是非完整的，因为诱导的非线性连接结构。最后，我们推测这样一种方法的量子化的关系曲线流和孤子的层次定义的爱因斯坦度量（伪）黎曼时空。
英文摘要：
The general relativity theory is redefined equivalently in almost Kahler variables: symplectic form and canonical symplectic connection (distorted from the Levi-Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metric on a manifold enabled with a necessary type nonholonomic 2+2 distribution. Such nonholonomic symplectic variables allow us to formulate the problem of quantizing Einstein gravity in terms of the A-model complexification of almost complex structures on spacetime manifold, generalizing the Gukov-Witten method, see arXiv:0809.0305. Quantizing the complexified model, we derive a Hilbert space as a space of strings with two A-branes which for the Einstein gravity theory are nonholonomic because of induced nonlinear connection structures. Finally, we speculate on relation of such a method of quantization to curve flows and solitonic hierarchies defined by Einstein metrics on (pseudo) Riemannian spacetimes.
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