On the phase diagram of 2d Lorentzian Quantum Gravity

The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal matter is studied. A phase transition is observed at $c=c_{\rm crit}$ ($1/2<c_{\rm crit}<4$) which can be thought of as the analogue of the $c=1$ barrier of Euclidean quantum gravity (EQG). The non--trivial properties of the quantum geometry are discussed.Comment: LATTICE99(gravity), 3 pages, espcrc2.sty, simulations available at http://www.nbi.dk/~ambjorn/lqg2

New critical phenomena in 2d quantum gravity

We study $q=10$ and $q=200$ state Potts models on dynamical triangulated lattices and demonstrate that these models exhibit continuous phase transitions, contrary to the first order transition present on regular lattices. For $q=10$ the transition seems to be of 2nd order, while it seems to be of 3rd order for $q=200$. For $q=200$ the phase transition also induces a transition between typical fractal structures of the piecewise linear surfaces corresponding to the triangulations. The typical surface changes from having a tree-like structure to a fractal structure characterizing pure gravity when the temperature drops below the critical temperature. An investigation of the alignment of spin clusters shows that they are strongly correlated to the underlying fractal structure of the triangulated surfaces.Comment: 22 pages, uuencoded compressed ps-file. Use csh file.uu to get ps-fil

Quantum rolling tachyon

We consider the quantum treatment of the rolling tachyon background describing the decay of D-branes in the limit of weak string coupling. We focus on the propagation of an open string in the fluctuating background and show how the boundary string action is modified by quantum effects. A bilocal term in the boundary action is generated which, however, does not spoil the vanishing of the $\beta$ function at one loop. The propagation of an open string for large times is found to be very strongly suppressed.Comment: 13 page

Strings, quantum gravity and non-commutative geometry on the lattice

I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods

Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization

We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search for a sensible continuum limit. For small values of the coupling constant of the $R^2$ term the model seems to belong to the same universality class as the model with pure Einstein-Hilbert action and exhibits the same phase transition. The order of the transition may be second or higher. The average curvature is positive at the phase transition, which makes it difficult to understand the possible scaling relations of the model.Comment: 27 pages (Latex), figures not included. Post script file containing 15 figures (1000 blocks) available from [email protected]

A Universal Fractal Structure of 2D Quantum Gravity for c > 1

We investigate the fractal structure of $2d$ quantum gravity coupled to matter by measuring the distributions of so-called baby universes. We demonstrate that the method works well as long as $c \leq 1$. For $c >1$ it is not clear what distribution to expect. However, we observe strikingly similar distributions for various kinds of matter fields with the same $c$. This indicate that there might be some range of $c >1$ where the central charge of the matter fields alone determines the fractal structure of gravity coupled to matter. The hypothesis that the string susceptibility \g = 1/3 is found to be compatible with the data for $1 < c \leq 4$.Comment: 12 pages. compressed postscript file. Uncompressed size 3 Mb. Latex file without figures available by request. NBI-HE-93-6

World-sheet dynamics of ZZ branes

We show how non-compact space-time (ZZ branes) emerges as a limit of compact space-time (FZZT branes) for specific ratios between the square of the boundary cosmological constant and the bulk cosmological constant in the (2,2m-1) minimal model coupled to two-dimensional quantum gravity.Comment: 14 page

The decay of quantum D-branes

We study the {\em quantum} decay of D0-branes in two-dimensional 0B string theory. The quantum nature of the branes provides a natural cut-off for the closed string emission rate. We find exact quantum mechanical wavefunctions for the decaying branes and show how one can include the effects of the Fermi sea for any string coupling (Fermi energy).Comment: 15 pages, 2 figure