5D共形不变引力中的自发对称性破缺
Spontaneous symmetry breaking in 5D conformally invariant gravity
摘要：
探讨了在5维共形不变引力中自发对称性破缺的可能性，其作用量由一个与曲率势非极小耦合的标量场组成.通过ADM分解进行降维，我们发现该模型允许一个精确的解决方案，从而产生4D Minkowski真空。利用带高斯弯曲因子的共形不变性，我们证明了它也存在一个实现共形对称自发破缺的解。通过对系统进行张量扰动，我们研究了系统的稳定性，发现系统可以用共形量子力学来描述。讨论了沿动力学第五方向的时间平移对称性的自发对称性破缺和膜世界情形的可能应用。
英文摘要：
We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implement the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting system is described by the conformal quantum mechanics. Possible applications to the spontaneous symmetry breaking of time-translational symmetry along the dynamical fifth direction and the brane-world scenario are discussed.
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