Minimizers of the dynamical Boulatov model

Understand

We study the Euler-Lagrange equation of the dynamical Boulatov model which is a simplicial model for 3d Euclidean quantum gravity augmented by a Laplace-Beltrami operator.

• We provide all its solutions on the space of left and right invariant functions that render the interaction of the model an equilateral tetrahedron.
• Surprisingly, for a non-linear equation of motion, the solution space forms a vector space.
• This space distinguishes three classes of solutions: saddle points, global and local minima of the action.