arXiv 1504.075732015-04-30gr-qchep-th

作为修正的Yang-Mills理论的二维引力

Two Dimensional Gravity as a modified Yang-Mills Theory

Jack Gegenberg, Gabor Kunstatter

备注：: 13 pages; references added

摘要：

我们研究了d-时空维的deSitter/Anti-deSitter/Poincare Yang-Mills引力理论，试图保留广义相对论和Yang-Mills理论的最佳特征：二次曲率、无量纲耦合和背景独立性。我们推导了李代数标量的运动方程，并证明了在几何光学极限下，它们相对于由框架场确定的洛伦兹几何穿过测地线。在WKB近似中，组分间的混合似乎接近于主导级。然后，为了简单起见，我们限制到两个时空维度，在这种情况下，理论简化为众所周知的Katanaev-Volovich模型。我们完成了真空理论的哈密顿分析，并用它证明了一个广义Birkhoff定理。有两类解：有挠和无挠。前者由两个运动常数参数化，在一定的参数范围内具有事件视界和曲率奇异性。后者产生一个唯一的解决方案，直到numeromorphisms，描述了一个空间常曲率。

英文摘要：

We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions for simplicity, in which case the theory reduces to the well known Katanaev-Volovich model. We complete the Hamiltonian analysis of the vacuum theory and use it to prove a generalized Birkhoff theorem. There are two classes of solutions: with torsion and without torsion. The former are parametrized by two constants of motion, have event horizons for certain ranges of the parameters and a curvature singularity. The latter yield a unique solution, up to diffeomorphisms, that describes a space constant curvature .

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摘要：

英文摘要：

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