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Free keywords:
General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
We study the the Euler-Lagrange equation of the dynamical Boulatov model,
which is a simplicial model for 3D 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 nonlinear equation, the solution space forms a vector
space. This space distinguishes three classes of solutions: saddle points,
global and local minima of the action. Our analysis shows that there exists one
parameter region of coupling constants, for which the action admits degenerate
global minima.
