Integrable 2D Lorentzian Gravity and Random Walks

Details Integrable 2D Lorentzian Gravity and Random Walks Integrable 2D Lorentzian Gravity and Random Walks

1999-07-12

arxiv.org/abs/hep-th/9907084v1

Nucl.Phys. B567 (2000) 515-553

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, 10 figures, harvmac, epsf

Scientific paper

10.1016/S0550-3213(99)00661-6

We introduce and solve a family of discrete models of 2D Lorentzian gravity with higher curvature, which possess mutually commuting transfer matrices, and whose spectral parameter interpolates between flat and curved space-times. We further establish a one-to-one correspondence between Lorentzian triangulations and directed Random Walks. This gives a simple explanation why the Lorentzian triangulations have fractal dimension 2 and why the curvature model lies in the universality class of pure Lorentzian gravity. We also study integrable generalizations of the curvature model with arbitrary polygonal tiles. All of them are found to lie in the same universality class.

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