arXiv 1202.63062012-02hep-thgr-qc

矩阵模型中的引力和紧化膜

Gravity and compactified branes in matrix models

Harold Steinacker

备注：: 35 pages. V2: substantially revised and improved, conclusion weakened. V3: some clarifications, published version. V4: minor correction
DOI：: 10.1007/JHEP07(2012)156

摘要：

展示了杨米尔斯矩阵模型中膜解上出现重力的机制。牛顿引力和爱因斯坦张量与能量动量张量之间的部分关系可以从基本矩阵模型作用量中产生，而不需要调用爱因斯坦-希尔伯特型项。关键的要求是紧化的额外维数，其外曲率为M^4 x K \subset R^D和分裂的非交换性，泊松张量θ^{ab}连接紧和非紧方向。紧化的模提供了引力的主导自由度，并通过泊松张量传递到4个非紧方向。有效牛顿常数由非交换性的尺度和紧化决定。这种引力理论非常适合量子化，并且被认为是IKKT模型的微扰有限。由于不需要对目标空间进行紧化，它可能提供了一种避免弦论中景观问题的方法。

英文摘要：

A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor θ^{ab} linking the compact with the noncompact directions. The moduli of the compactification provide the dominant degrees of freedom for gravity, which are transmitted to the 4 noncompact directions via the Poisson tensor. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it might provide a way to avoid the landscape problem in string theory.

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