Mother canonical tensor model

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.

31 pages, 8 figures; a paragraph added on uniqueness, references updated, minor changes of expressions, typos corrected

References in corpus (12)

• Critical phenomena in complex networks
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Physical states in the canonical tensor model from the perspective of random tensor networks
• Tensor networks for dynamic spacetimes
• Random Holographic "Large Worlds" with Emergent Dimensions
• Emergent Space-Time via a Geometric Renormalization Method
• Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
• Space-time and special relativity from causal networks
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• Emergent classical geometries on boundaries of randomly connected tensor networks
• Thesis: Tensor networks for dynamic spacetimes

Cited by in corpus (1)

• Emergent symmetries in the canonical tensor model