Tensor models and hierarchy of n-ary algebras

Details Tensor models and hierarchy of n-ary algebras Tensor models and hierarchy of n-ary algebras

2011-04-28

arxiv.org/abs/1104.5312v2

Int.J.Mod.Phys.A26:3249-3258,2011

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, some references updated and corrected

Scientific paper

10.1142/S0217751X1105381X

Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator, and the 3-ary algebra symmetry reported in the previous paper is just a single sector of the whole structure. The condition for the Leibnitz rules of the n-ary algebras is discussed from the perspective of the invariance of the underlying algebra under the n-ary transformations. It is shown that the n-ary transformations which keep the underlying algebraic structure invariant form closed finite n-ary Lie subalgebras. It is also shown that, in physical settings, the 3-ary transformation practically generates only local infinitesimal symmetry transformations, and the other more non-local infinitesimal symmetry transformations of the tensor models are generated by higher n-ary transformations.

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