Talk presented by Konstantinos Anagnostopoulos

Parallel Session: Gravity and Random Surfaces

Friday July 2nd, 14.30 - 14.50, Room 6

Taking 2d Lorentzian quantum gravity seriously

Abstract: In the investigation of discrete models of quantum gravity, the fundamental problem of a suitable continuation from Euclidean to Lorentzian metric signature has in the past received only scant attention. In two space-time dimensions, a Lorentzian model for pure gravity has recently been put forward and solved analytically [1]. Somewhat surprisingly, this leads to a well-defined continuum theory inequivalent to the usual Liouville gravity. It presents a genuinely alternative quantum gravity theory in two dimensions, which incorporates a notion of causality and a distinguished time direction. Since the discrete formulation is just a variant of the dynamical triangulations approach, we have set up Monte Carlo simulations to study the behaviour of geometry and matter coupled to geometry in this model [2]. For pure gravity, they illustrate beautifully our analytic findings that the quantum geometry - in spite of strong fluctuations - is much smoother than in the Liouville case, with Hausdorff dimension 2. Adding Ising spins to the model, we find only a weak coupling between matter and geometry, which leaves the Hausdorff dimension unchanged. The critical matter behaviour is governed by the Onsager exponents, in agreement with the results of a high-temperature expansion. We conclude that also in the matter-coupled case the Lorentzian model remains stable, well-behaved, and readily interpretable in terms of classical notions of geometry. This makes it an attractive alternative to Liouville quantum gravity.

Valid HTML 3.2!     Massimo Campostrini,   campo@mailbox.difi.unipi.it