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Minimizers of the dynamical Boulatov model

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Geloun,  Joseph Ben
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Kegeles,  Alexander
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Pithis,  Andreas G. A.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1806.09961.pdf
(Preprint), 697KB

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Citation

Geloun, J. B., Kegeles, A., & Pithis, A. G. A. (2018). Minimizers of the dynamical Boulatov model. European Physical Journal C, 78(12): 996. doi:10.1140/epjc/s10052-018-6483-8.


Cite as: http://hdl.handle.net/21.11116/0000-0001-DC20-3
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.