Tensor Model for Gravity and Orientability of Manifold

Abstract

We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

The bulk dual of SYK: cubic couplings

“…The simplest is to make the couplings Ji 1 ...iq be nearly static quantum variables [28]. A better way of eliminating disorder is to turn SYK into a tensor model [29] (see also, [30][31][32]), analogous to the ones previously studied [33][34][35][36][37]. To leading order in 1/N all these approaches agree.…”

Tensorial Methods and Renormalization in Group Field Theories

“…The success of matrix models motivated extensions to higher dimensions already in the nineties, called tensor models [53][54][55]. Viewing a matrix as a 2-tensor, it is natural to introduce d-tensors in d dimensions.…”

Random volumes from matrices

“…Tensor models [20][21][22] or group field theory [23,24] are natural generalizations of matrix models to three (and higher) dimensions. For three-dimensional models, the perturbative expansion generates random tetrahedral decompositions of three-dimensional objects.…”

“…Thus, the value of a closed index loop forming -gon changes from tr 1 n = n = 3m to tr(ω ) = n ( = 0 mod 3) 0 ( = 0 mod 3). (3.11) 21 Although we only discuss the case A = M3m(R), we can also introduce the color structure to other algebras by taking the tensor product of the form R = (A ⊗ M3(R)) ⊗ (Ā ⊗ M3(R)). Note that Mm(R) ⊗ M3(R) = M3m(R).…”