论文标题
局部规模不变kaluza-klein减少
Local Scale Invariant Kaluza-Klein Reduction
论文作者
论文摘要
我们执行4维kaluza-klein（kk）局部局部规模不变的Weyl-Dirac重力的还原。尽管不可避免地将紧凑的长度尺度引入了该理论，但它以一种可以从低能量制度将KK半径整合在一起的方式，从而使KK真空仍然可以在经典层面享受局部规模的不变性。模仿$ u（1）\ times \ tilde {u}（1）$量学理论，新兴的4D理论的特征是动力学的麦克斯韦 - 韦尔·混合，其对角线化过程详细地进行了。特别是，我们确定了定义4D Weyl载体的唯一线性组合，并将4D标量扇区完全分类。后者包括（使用Weyl语言）一个共同量表和两个刻板座。该分析是针对一般KK $ M $ -ANSATZ执行的，该分析由标量场的功率$ M $进行参数，该电源分配了4D公制。例如，满足了NO-GHOST要求，提供了$ - \ frac {1} {2} \ leq m \ leq 0 $。然后在原始的5D Brans-Dicke参数$ω_5$和由此产生的4D $ω_4$之间建立了$ m $依赖性词典。关键$ω_5= - \ frac {4} {3} $始终映射到关键$ω_4= - \ frac {3} {2} $。 KK减少的Maxwell-Weyl动力学混合无法缩放，因为它是由4D量表介导的（位于5D Weyl Vector中）。在爱因斯坦框架内明确证明了混合，以特殊的出于物理动机的选择为$ m = - \ frac {1} {3} $。例如，超临界的Brans-Dicke参数会引起对原始（如果通过5维标量电势引入）宇宙常数的微小阳性贡献。最后，在通用的迷你苏普斯空间水平上研究了一些无规模的量子宇宙学方面。
We perform the 4-dimensional Kaluza-Klein (KK) reduction of the 5-dimensional locally scale invariant Weyl-Dirac gravity. While compactification unavoidably introduces an explicit length scale into the theory, it does it in such a way that the KK radius can be integrated out from the low energy regime, leaving the KK vacuum to still enjoy local scale invariance at the classical level. Imitating a $U(1)\times\tilde{U}(1)$ gauge theory, the emerging 4D theory is characterized by a kinetic Maxwell-Weyl mixing whose diagonalization procedure is carried out in detail. In particular, we identify the unique linear combination which defines the 4D Weyl vector, and fully classify the 4D scalar sector. The later consists of (using Weyl language) a co-scalar and two in-scalars. The analysis is performed for a general KK $m$-ansatz, parametrized by the power $m$ of the scalar field which factorizes the 4D metric. The no-ghost requirement, for example, is met provided $-\frac{1}{2}\leq m \leq 0$. An $m$-dependent dictionary is then established between the original 5D Brans-Dicke parameter $ω_5$ and the resulting 4D $ω_4$. The critical $ω_5=-\frac{4}{3}$ is consistently mapped into critical $ω_4 = -\frac{3}{2}$. The KK reduced Maxwell-Weyl kinetic mixing cannot be scaled away as it is mediated by a 4D in-scalar (residing within the 5D Weyl vector). The mixing is explicitly demonstrated within the Einstein frame for the special physically motivated choice of $m=-\frac{1}{3}$. For instance, a super critical Brans-Dicke parameter induces a tiny positive contribution to the original (if introduced via the 5-dimensional scalar potential) cosmological constant. Finally, some no-scale quantum cosmological aspects are studied at the universal mini-superspace level.
