标题： 关于法德耶夫引力中的面积谱 显示英文标题

标题： On area spectrum in the Faddeev gravity

摘要： 我们考虑引力的法捷耶夫形式，其中度规是$d = 10$四维矢量场的双线性式。 这种形式的一个独特特点是，对于不连续的场，作用量仍然是有限的（尽管在运动方程中恢复了连续性）。 这意味着时空可以分解为几乎不在公共面上重合的4单纯形，即独立的。 这特别允许将一个曲面视为由一组几乎独立的基本部分（2单纯形）组成。 那么曲面面积的谱就是独立基本面积谱的和。 我们使用之前在我们的工作中提出的分段平坦（单纯形）流形的法捷耶夫作用量的连接表示。 基本面积的谱是与正交连接矩阵共轭的场双线性式的谱。 我们发现，基本面积的谱在法捷耶夫引力中与巴贝罗-伊梅尔齐参数$\gamma$成比例，并且类似于维度为$d - 2$的空间中的角动量谱。 了解这个谱允许估算统计黑洞熵。 要求该熵与贝肯斯坦-霍金熵一致给出了文献中已知的方程。 这个方程允许对任意的$d$估算$\gamma$，特别是对真实的$d = 10$估算$\gamma = 0.39...$。 显示英文摘要

摘要： We consider Faddeev formulation of gravity, in which the metric is bilinear of $d = 10$ 4-vector fields. A unique feature of this formulation is that the action remains finite for the discontinuous fields (although continuity is recovered on the equations of motion). This means that the spacetime can be decomposed into the 4-simplices virtually not coinciding on their common faces, that is, independent. This allows, in particular, to consider a surface as consisting of a set of virtually independent elementary pieces (2-simplices). Then the spectrum of surface area is the sum of the spectra of independent elementary areas. We use connection representation of the Faddeev action for the piecewise flat (simplicial) manifold earlier proposed in our work. The spectrum of elementary areas is the spectrum of the field bilinears which are canonically conjugate to the orthogonal connection matrices. We find that the elementary area spectrum is proportional to the Barbero-Immirzi parameter $\gamma$ in the Faddeev gravity and is similar to the spectrum of the angular momentum in the space with the dimension $d - 2$. Knowing this spectrum allows to estimate statistical black hole entropy. Requiring that this entropy coincide with the Bekenstein-Hawking entropy gives the equation, known in the literature. This equation allows to estimate $\gamma$ for arbitrary $d$, in particular, $\gamma = 0.39...$ for genuine $d = 10$.