Discrete gravitational dimensions
Discrete gravitational dimensions
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离散重力维度
DOI：
10.1103/physrevd.69.104001
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发表时间：
2003
影响因子：
5
通讯作者：
M. Schwartz
中科院分区：
文献类型：
--
作者：
N. Arkani;M. Schwartz
我们用大质量引力子的有效场论研究了单个离散引力额外维的物理。我们首先考虑一个最小的离散与四维引力子的网站和最近邻跳跃项。在线性水平上，5D连续物理被正确地恢复，但在非线性水平上，理论在离散维中变得高度非局部。有一个特殊的紫外/红外连接，在高能量下强相互作用的尺度与维度的半径有关。这些新的效应在零晶格间距的极限下正式消失，但没有足够快地在有效场论中一致地再现连续介质物理直到5D普朗克尺度。尽管如此，这个模型作为一个有效的理论，在参数上高于紧致化尺度的能量上是有意义的。为了有一个在连续极限中局部出现的离散理论，晶格作用量必须在遥远的位置之间有相互作用。我们推测的相关性，这些意见的建设有限离散理论的引力在四维空间。
We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At the linear level, 5D continuum physics is recovered correctly, but at the nonlinear level the theory becomes highly nonlocal in the discrete dimension. There is a peculiar UV/IR connection, where the scale of strong interactions at high energies is related to the radius of the dimension. These new effects formally vanish in the limit of zero lattice spacing, but do not do so quickly enough to reproduce the continuum physics consistently in an effective field theory up to the 5D Planck scale. Nevertheless, this model does make sense as an effective theory up to energies parametrically higher than the compactification scale. In order to have a discrete theory that appears local in the continuum limit, the lattice action must have interactions between distant sites. We speculate on the relevance of these observations to the construction of finite discrete theories of gravity in four dimensions.