论文标题
关于公制与公制的重力的评论
A comment on Metric vs Metric-Affine Gravity
论文作者
论文摘要
我们考虑Einstein-Hilbert Action和Pontryagin密度（PD）的总和，甚至是任意尺寸$ D $。所有曲率仅是独立仿射（无扭转）连接的函数。在任意维度中，不仅在$ d = 4n $中，这些一阶PD项被证明是“ Chern-Simons”电流的协方差差异。连接的场方程导致其是Levi-civita，并且指标和仿射场方程等同于二阶度量理论。该结果是与定理的反例，表明纯度公制和公制模型仅适用于lovelock理论。
We consider the sum of the Einstein-Hilbert action and a Pontryagin density (PD) in arbitrary even dimension $D$. All curvatures are functions of independent affine (torsionless) connections only. In arbitrary dimension, not only in $D=4n$, these first order PD terms are shown to be covariant divergences of "Chern-Simons" currents. The field equation for the connection leads to it being Levi-Civita, and to the metric and affine field equations being equivalent to the second order metric theory. This result is a counterexample to the theorem stating that purely metric and metric-affine models can only be equivalent for Lovelock theories.
