庞加莱对称厚膜上的质量等级、质量间隙和对牛顿定律的修正
Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry
摘要：
我们考虑一个标量厚膜配置产生的引力耦合到一个自相互作用的标量场在黎曼流形的5D理论。我们从已知的相应的场方程的经典解出发，详细阐述了经典背景的线性波动的横向无痕模式的物理学，它服从薛定谔方程。我们进一步考虑了两种特殊情况，在这两种情况下，与数值方法相比，对于任何m^2>0的质量模，这个方程都可以解析求解，这使我们能够以封闭形式研究卡鲁扎-克莱因（KK）激发的质量谱，并计算薄膜极限下牛顿定律的修正。在第一种情况下，我们考虑一个解决方案的质量差距的频谱中的KK波动与两个束缚态-无质量的四维引力子免费的快子不稳定性和大规模的KK激发-以及塔的连续大规模KK模式，服从勒让德方程。质量间隙是由膜厚度的倒数定义的，这使我们能够摆脱任意轻KK模式的潜在危险的多重性。结果表明，由于这种幸运的情况下，解决的质量等级问题是更简单和透明的比（薄）兰德尔Sundrum（RS）的两膜配置。在第二种情况下，我们提出了一个光滑的版本的RS模型与一个单一的无质量的束缚态，它占的4D引力子，和一个部门的连续波动模式，没有质量间隙，服从合流Heun方程在Ince极限。(The后者似乎第一次在膜世界模型中具有物理应用）。对于这个解决方案的质量层次问题解决的Lykken-Randall模型和模型是完全免费的裸奇点。
英文摘要：
We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.
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