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Canonical tensor model (CTM for short below) is a rank-three tensor modelformulated as a totally constrained system in the canonical formalism. In theclassical case, the constraints form a first-class constraint Poisson algebrawith structures similar to that of the ADM formalism of general relativity,qualifying CTM as a possible discrete formalism for quantum gravity. In thispaper, we show that, in a formal continuum limit, the constraint Poissonalgebra of CTM with no cosmological constant exactly reproduces that of the ADMformalism. To this end, we obtain the expression of the metric tensor field ingeneral relativity in terms of one of the dynamical rank-three tensors in CTM,and determine the correspondence between the constraints of CTM and those ofthe ADM formalism. On the other hand, the cosmological constant term of CTMseems to induce non-local dynamics, and is inconsistent with an assumptionabout locality of the continuum limit.

Constraint algebra of general relativity from a formal continuum limit of canonical tensor model