论文标题
封闭的爱因斯坦歧管上的引导程序边界
Bootstrap Bounds on Closed Einstein Manifolds
论文作者
论文摘要
紧凑的Riemannian歧管与由Laplacian算子在歧管上的特征值和相应特征码的三重重叠积分上给出的几何数据相关。该几何数据必须满足从关联性和本本征的完整性随之而来的某些一致性条件。我们表明，可以通过使用半芬矿编程来研究这些一致性条件，以类似于保形场理论上的保形性自举界，可以在封闭的爱因斯坦歧管的几何数据上获得非平凡的界限。这些引导程序边界转化为在具有紧凑的额外尺寸的理论中Kaluza-Klein模式的树级质量和立方耦合的约束。我们表明，在某些情况下，边界被已知歧管饱和。
A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.
