Phase transitions in group field theory: The Landau perspective

Understand

In various approaches to quantum gravity continuum spacetime is expected to emerge from discrete geometries through a phase transition.

• In group field theory, various indications for such a transition have recently been found but a complete understanding of such a phenomenon remains an open issue.
• In this work, we investigate the critical behavior of different group field theory models in the Gaussian approximation.
• Applying the Ginzburg criterion to quantify field fluctuations, we find that this approximation breaks down in the case of three-dimensional Euclidean quantum gravity as described by the dynamical Boulatov model on the compact group $\text{SU}(2)$.