Mother canonical tensor model

TL;DR

This paper introduces a 'mother' tensor model (mCTM) that derives the canonical tensor model (CTM) via the Hamilton-Jacobi formalism, providing new insights into its structure, constraints, and potential dynamics.

Contribution

The paper constructs a 'mother' tensor model (mCTM) that generates CTM through the Hamilton-Jacobi approach and explores its classical and quantum solutions, revealing richer dynamics.

Findings

Found exact physical wave functions solving constraints.

Identified classical phase spaces consistent with constraints.

Demonstrated mCTM's richer dynamics compared to CTM.

Abstract

Canonical tensor model (CTM) is a tensor model formulated in the Hamilton formalism as a totally constrained system with first class constraints, the algebraic structure of which is very similar to that of the ADM formalism of general relativity. It has recently been shown that a formal continuum limit of the classical equation of motion of CTM in a derivative expansion of the tensor up to the fourth derivatives agrees with that of a coupled system of general relativity and a scalar field in the Hamilton-Jacobi formalism. This suggests the existence of a "mother" tensor model which derives CTM through the Hamilton-Jacobi procedure, and we have successfully found such a "mother" CTM (mCTM) in this paper. The quantization of mCTM is straightforward as CTM. However, we have not been able to identify all the secondary constraints, and therefore the full structure of the model has been left for future study. Nonetheless, we have found some exact physical wave functions and classical phase spaces which can be shown to solve the primary and all the (possibly infinite) secondary constraints in the quantum and classical cases, respectively, and have thereby proven the non-triviality of the model. It has also been shown that mCTM has more interesting dynamics than CTM from the perspective of randomly connected tensor networks.