A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
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abstract
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d continuum gravity in proper-time gauge, but it disagrees with 2d gravity defined via matrix models or Liouville theory. By allowing topology change of the compact spatial slices (i.e. baby universe creation), one obtains agreement with the matrix models and Liouville theory.
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Authors introduce simplicial-complex matrices and genetic mutation/crossover operations on them to algorithmically generate pseudomanifolds of varied topologies and compute simplex volumes and circumcenters.
Topological recursion solves Schwinger-Dyson equations for multicritical and causal dynamical triangulations in 2D quantum gravity, yielding explicit amplitudes.
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The perturbative Ricci flow in gravity
A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.
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Mutation and crossover of simplicial complexes
Authors introduce simplicial-complex matrices and genetic mutation/crossover operations on them to algorithmically generate pseudomanifolds of varied topologies and compute simplex volumes and circumcenters.
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Multicritical Dynamical Triangulations and Topological Recursion
Topological recursion solves Schwinger-Dyson equations for multicritical and causal dynamical triangulations in 2D quantum gravity, yielding explicit amplitudes.