Galloway G J, Surya S, Woolgar E
Department of Mathematics, University of Miami, Coral Gables, Florida 33124, USA.
Phys Rev Lett. 2002 Mar 11;88(10):101102. doi: 10.1103/PhysRevLett.88.101102. Epub 2002 Feb 25.
The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons, this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the anti-de Sitter (AdS) soliton, a globally static, asymptotically toroidal Lambda<0 spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static Lambda<0 spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.
物理系统的稳定性取决于最低能量状态的存在。在引力中，这由正能量定理保证。出于拓扑原因，对于非超对称卡鲁扎 - 克莱因紧致化情形这并不成立，这种情况下系统可能衰变为任意负能量。出于相关原因，对于反德西特（AdS）孤子这也不成立，反德西特孤子是一个全局静态、渐近为环面的Λ<0时空且具有负质量。尽管如此，基于反德西特共形场论（AdS/CFT）对应关系，霍洛维茨和迈尔斯提出了一个新的正能量猜想，该猜想断言反德西特孤子是其渐近类中唯一的最低能量状态。我们给出了一个关于静态Λ<0时空的新结构定理，并利用它证明了反德西特孤子的唯一性。我们的结果为新的正能量猜想提供了重要支持，并丰富了受AdS/CFT对应关系启发得出的严格结果。
