标题： 引力中的隐藏对称性：黑洞和其他迷你超空间 显示英文标题

标题： Hidden Symmetries in Gravity : Black holes and other minisuperspaces

摘要： 本论文致力于研究引力简化模型中的对称性，其中一些自由度被冻结。 我们关注具有有限自由度的极小超空间约化。 极小超空间被当作机械模型来处理，在一个时空方向上演化。 这个演化参数代表了时空均匀叶层分解的正交坐标。 我研究了它们的经典对称性以及相应诺特定理守恒量的代数结构。 在介绍了允许我们通过作用原理描述简化模型的形式之后，我们讨论了具有（扩展）共形对称性的条件。 特别是，黑洞模型阐明了均匀切片的空间边界所起的微妙作用。 后者与共形对称性相互作用，从机械观点来看，它与一个守恒量相关。 由于对称性破缺机制，这里没有全理论中特有的无限阶荷塔。 通过观察对称群的无限维扩展可以明确这一点。 这使得我们可以从无限维群的角度来看待机械系统的运动方程，而该群反过来有重标理论耦合常数的效果。 最后，有限对称群的存在允许根据相应的表示理论定义量子模型。 在有效理论层面，考虑到量子效应，要求对称性得到保护提供了一个强大的工具，用于区分不同的修改方案。 最终，黑洞背景的共形不变性打开了其全息性质的大门，并可能在相应的微扰理论中产生重要影响。 显示英文摘要

摘要： This thesis is dedicated to the study of symmetries in reduced models of gravity, with some frozen degrees of freedom. We focus on the minisuperspace reduction whith a finite number of degrees of freedom. Minisuperspaces are treated as mechanical models, evolving in one spacetime direction. This evolution parameter represents the orthogonal coordinate to the homogeneous foliation of the spacetime. I investigate their classical symmetries and the algebra of the corresponding Noether charges. After presenting the formalism allowing us to describe the reduced models in terms of an action principle, we discuss the condition for having an (extended) conformal symmetry. In particular, the black hole model enlightens the subtle role of the spacelike boundary of the homogeneous slice. The latter interplays with the conformal symmetry, being associated with a conserved quantity from the mechanical point of view. The absence of the infinite tower of charges, characteristic of the full theory, is due here to a symmetry-breaking mechanism. This is made explicit by looking at the infinite-dimensional extension of the symmetry group. This allows to look at the equation of motion of the mechanical system in terms of the infinite-dimensional group, who in turn has the effect of rescaling the coupling constants of the theory. Finally, the presence of the finite symmetry group allows defining a quantum model in terms of the corresponding representation theory. At the level of the effective theory, accounting for the quantum effects, the request that the symmetry is protected provides a powerful tool to discriminate between different modifications. In the end, the conformal invariance of the black hole background opens the door to its holographic properties and might have important consequences in the corresponding perturbation theory.