Putting a cap on causality violations in causal dynamical triangulations

The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum limits have been studied in two, three and four dimensions. Here we investigate a generalization of the two-dimensional CDT model, where the causality constraint is partially lifted by introducing branching points with a weight g s, and demonstrate that the system can be solved analytically in the genus-zero sector. The solution is analytic in a neighborhood around weight g s = 0 and cannot be analytically continued to g s = , where the branching is entirely geometric and where one would formally recover standard Euclidean two-dimensional quantum gravity defined via dynamical triangulations or Liouville theory. © SISSA 2007