Integrable 2D Lorentzian gravity and random walks

P. Di Francesco, E. Guitter, C. Kristjansen

Research output: Contribution to journalArticlepeer-review


We introduce and solve a family of discrete models of 2D Lorentzian gravity with higher curvature weight, 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.

Original languageEnglish (US)
Pages (from-to)515-553
Number of pages39
JournalNuclear Physics B
Issue number3
StatePublished - Feb 21 2000
Externally publishedYes


  • Integrable models
  • Lorentzian triangulations
  • Quantum gravity
  • Random walks

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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