自完备性与自发降维
Self-completeness and spontaneous dimensional reduction
摘要：
一个可行的引力量子理论是物理学家面临的最大挑战之一。我们讨论了两个高度期望的功能，这可能是在有限的和可重整化的量子引力的追求工具的汇合-自发降维和自完备性。前者表明普朗克尺度下的时空背景可能是有效的二维，而后者则意味着物质通过形成普朗克散射的事件视界而受到最大压缩的条件。我们将这样的结果推广到任意数量的维度，并表明，在高于四维的引力保持自我完整，但在较低的维度，它不是。通过这种方式，我们在自完备性和降维的发生之间建立了一个“异或”或“异或”（XOR），目标是实际减少普朗克尺度物理学场景的未知数。潜在的唯象影响，这一结果被认为是通过研究的情况下，一个二维的Einstein引力降维引力模型产生的。
英文摘要：
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.
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