Federico Capone, Prahar Mitra, Aaron Poole, Bilyana Tomova
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引用次数: 6
摘要
我们对六维爱因斯坦引力的解空间进行了完整而系统的分析。我们证明了在$$ \mathcal{I} $$ I +附近解析解的一个特殊子类承认包含无限维超平移和超旋转的广义Bondi-Metzner-van der Burg-Sachs (GBMS)群的非平凡作用。后者由天体s4的所有光滑的体积保持Diff×Weyl变换组成。利用协变相空间形式和本文提出的一种新技术(相空间重整化),我们可以用局部协变的反项对辛势进行重整化。对应于GBMS微分同胚的哈密顿电荷是不可积的。我们证明了这些电荷的可积部分忠实地表示了GBMS代数,从而解决了一个长期存在的关于高偶数维非线性重力中无限维渐近对称性的存在性的开放性问题。最后,我们证明了超平移和超旋转的半经典Ward恒等式分别是软引力子的先导定理和次先导定理。
Phase space renormalization and finite BMS charges in six dimensions
A bstract We perform a complete and systematic analysis of the solution space of six-dimensional Einstein gravity. We show that a particular subclass of solutions — those that are analytic near $$ \mathcal{I} $$ I + — admit a non-trivial action of the generalised Bondi-Metzner-van der Burg-Sachs (GBMS) group which contains infinite-dimensional supertranslations and superrotations. The latter consists of all smooth volume-preserving Diff×Weyl transformations of the celestial S 4 . Using the covariant phase space formalism and a new technique which we develop in this paper (phase space renormalization), we are able to renormalize the symplectic potential using counterterms which are local and covariant . The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries in higher even dimensional non-linear gravity. Finally, we show that the semi-classical Ward identities for supertranslations and superrotations are precisely the leading and subleading soft-graviton theorems respectively.
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