arXiv 1407.59772014-07hep-thgr-qcmath.DG

量子引力是陈-西蒙斯理论吗？

Is Quantum Gravity a Chern-Simons Theory?

R. Bonezzi, O. Corradini, A. Waldron

备注：: 22 pages, LaTeX, 3 figures, references added, version to appear in PRD
DOI：: 10.1103/PhysRevD.90.084018

摘要：

我们提出了一个任意维的量子引力模型，它是由超对称无限维矩阵模型的BV量子化定义的。这给出了一个具有规范代数的（AKSZ-型）陈-西蒙斯理论，该理论是量子力学希尔伯特空间H的可观测量空间。该模型的动机是以前的尝试，制定重力的非交换，相空间，场论，以及费曼-格雷厄姆弯曲模拟的狄拉克空间共形不变的波动方程。场方程是等于零曲率的平坦连接条件和作用在H上的算子的平行条件。这种矩阵型模型可以为量子引力的路径积分提供更好的定义。我们证明了它的基本物理是一个由共形类度量标记的哈密顿算子的求和，因此是因果结构的求和。这反过来又给出了一个模型，加上一个额外的模式塔的波动指标求和-我们推测，这些可以产生改进的UV行为。

英文摘要：

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, field theories as well as the Fefferman-Graham curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on H. This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes-we speculate that these could yield improved UV behavior.

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。

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英文摘要：

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