Crossing the c=1 barrier in 2d Lorentzian quantum gravity
Crossing the c=1 barrier in 2d Lorentzian quantum gravity
复制标题
跨越二维洛伦兹量子引力中的 c=1 势垒
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Loll
中科院分区：
文献类型：
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作者：
J. Ambjrn;K. Anagnostopoulos;R. Loll
在早期工作的扩展中，我们研究了二维洛伦兹量子引力在与c > 1的共形场论耦合时的行为。这是通过数值分析一个系统的八个伊辛模型（对应于c=4）耦合到动态三角洛伦兹几何。众所周知，单个伊辛模型与洛伦兹量子引力的耦合很弱，在这个意义上，两个几何的系综的豪斯多夫维数是2（就像在纯洛伦兹量子引力中一样），物质的行为由昂萨格指数决定。通过增加物质的数量到8个伊辛模型，我们发现组合系统的几何形状发生了相变。新相的特征是在大距离处空间长度相对于适当时间的异常标度，因此豪斯多夫维数现在是3。尽管几何部分发生了质的变化，物质和几何之间存在着非常强的相互作用，伊辛模型的临界指数仍然保持着它们的昂萨格值。这为猜想提供了证据，即2d欧几里德量子引力中临界指数的KPZ值完全是由于婴儿宇宙的存在。最后，我们总结了迄今为止从2d洛伦兹量子引力中所学到的经验教训。
In an extension of earlier work we investigate the behaviour of two-dimensional Lorentzian quantum gravity under coupling to a conformal field theory with c > 1. This is done by analyzing numerically a system of eight Ising models (corresponding to c=4) coupled to dynamically triangulated Lorentzian ge- ometries. It is known that a single Ising model couples weakly to Lorentzian quantum gravity, in the sense that the Hausdorff dimension of the ensemble of two-geometries is two (as in pure Lorentzian quantum gravity) and the matter behaviour is governed by the Onsager exponents. By increasing the amount of matter to 8 Ising models, we find that the geometry of the combined system has undergone a phase transition. The new phase is characterized by an anomalous scaling of spatial length relative to proper time at large distances, and as a consequence the Hausdorff dimension is now three. In spite of this qualitative change in the geometric sector, and a very strong interaction between matter and geometry, the critical exponents of the Ising model retain their Onsager values. This provides evidence for the conjecture that the KPZ values of the critical exponents in 2d Euclidean quantum gravity are entirely due to the presence of baby universes. Lastly, we summarize the lessons learned so far from 2d Lorentzian quantum gravity.