论文标题
非交易性$ d = 5 $ Chern-Simons重力：Kaluza-Klein减少和手性重力异常
Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
论文作者
论文摘要
使用普通古典字段及其NC对应物之间的Seiberg-Witten Map，可以在非交通量参数$θ$的功能上触及扰动地扩展非交通（NC）仪表理论的动作。领先的订单项代表经典（$θ= 0 $）的操作，而高阶项给出了US $θ$依赖的NC校正，应捕获量子重力的某些方面。 Building on previous work of Aschieri and Castellani on NC Chern-Simons (CS) gauge and gravity theories, showing that non-trivial $θ$-dependence exists only for spacetime dimensions $D\geq 5$, we investigate a correlated effect of these extra spatial dimensions and noncommutativity on four-dimensional physics, up to first-order in $θ$.假设一个空间维度被压缩到一个圆圈中，我们将kaluza-klein降低程序应用于NC $ d = 5 $ d = 5 $ cs的理论，用于保形规组$ so so（4,2）$，以获得有效的，$θ$依赖性的四维重力理论，其具有负效率的cosmolbert cosmological cosmompitivate cosmmological cosmompitive and consmomptical cosmompitiation consmm consimutical consm consutcriptication consm consutcriptication。我们得出了这种修改的重力理论的场方程，并研究了NC相互作用对某些经典几何形状的影响，例如ADS-SCHWARZSCHILD黑洞。我们发现，由于不存在$θ$依赖性的Pontryagin密度，这种NC背景时空会引起手性重力异常。
Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter $θ$ using the Seiberg-Witten map between ordinary classical fields and their NC counterparts. The leading order term represents classical ($θ=0$) action while higher-order terms give us $θ$-dependent NC corrections that ought to capture some aspects of quantum gravity. Building on previous work of Aschieri and Castellani on NC Chern-Simons (CS) gauge and gravity theories, showing that non-trivial $θ$-dependence exists only for spacetime dimensions $D\geq 5$, we investigate a correlated effect of these extra spatial dimensions and noncommutativity on four-dimensional physics, up to first-order in $θ$. Assuming that one spatial dimension is compactified into a circle, we apply the Kaluza-Klein reduction procedure on the NC $D=5$ CS theory for the conformal gauge group $SO(4,2)$, to obtain an effective, $θ$-dependent four-dimensional theory of gravity that has Einstein-Hilbert gravity with negative cosmological constant as its commutative limit. We derive field equations for this modified theory of gravity and study the effect of NC interactions on some classical geometries, such as the AdS-Schwarzschild black hole. We find that this NC background spacetime gives rise to chiral gravitational anomaly due to the nonvanishing $θ$-dependent Pontryagin density.
