Minimizers of the dynamical Boulatov model

TY - JOUR

T1 - Minimizers of the dynamical Boulatov model

AU - Geloun, Joseph Ben

AU - Kegeles, Alexander

AU - Pithis, Andreas G. A.

N1 - closest to published version

PY - 2018/6/26

Y1 - 2018/6/26

N2 - 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. Our analysis shows that there exists one parameter region of coupling constants for which the action admits degenerate global minima.

AB - 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. Our analysis shows that there exists one parameter region of coupling constants for which the action admits degenerate global minima.

KW - gr-qc

KW - hep-th

KW - math-ph

KW - math.MP

U2 - 10.1140/epjc/s10052-018-6483-8

DO - 10.1140/epjc/s10052-018-6483-8

M3 - Article

JO - Eur. Phys. J. C

JF - Eur. Phys. J. C

ER -