Interpreting canonical tensor model in minisuperspace

Sasakura, Naoki; Sato, Yuki

doi:10.1016/j.physletb.2014.03.006

Cited by 30 publications

(53 citation statements)

References 38 publications

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“…The fundamental dynamical variables of the model are a conjugate pair of real symmetric rank-3 tensors. The CTM has been shown to have a strong connection to general relativity: It agrees with a mini-superspace approximation for N = 1 [18], 3 while in a formal continuum limit, where N → ∞, the dynamical structure agrees with that of general relativity [19,20]. Due to this connection with general relativity and the fact that the model can be quantized easily [21], one can hope for this model to be a consistent model for quantum gravity.…”

Section: Introductionmentioning

confidence: 74%

“…Therefore, the solution is more non-trivial than (17) in the P representation, which is a solution to the first order ones. Unfortunately, we do not presently have any generalization of this solution to λ = 0.13 λ corresponds to the cosmological constant in the correspondence between the CTM with N = 1 and the minisuperspace treatment of general relativity[18]. Therefore, the necessity of λ > 0 is curiously matching the present astrophysical observation of a positive cosmological constant.…”

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confidence: 90%

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Emergent symmetries in the canonical tensor model

Obster

Sasakura

2018

Progress of Theoretical and Experimental Physics

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The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent model of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. A recent study on the formal continuum limit of the classical CTM has shown that it produces a general relativistic system. This formal continuum limit assumes the emergence of a continuous space, but ultimately continuous spaces should be obtained as preferred configurations of the quantum CTM. In this paper we study the symmetry properties of a wave function which exactly solves the quantum constraints of the CTM for general N . We have found that it has strong peaks at configurations invariant under some Liegroups, as predicted by a mechanism described in our previous paper. A surprising result was the preference of configurations invariant not only under Lie-groups with positive signatures, but also with spacetime-like signatures, i.e., SO(1, n). Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behaviour, which for the most part seems to be well under control.

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Section: Introductionmentioning

confidence: 74%

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confidence: 90%

Emergent symmetries in the canonical tensor model

Obster

Sasakura

2018

Progress of Theoretical and Experimental Physics

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“…In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal symmetry, while the time evolution of the scale factor is power-law in dimensions below six.1 See, however,[4,5,6] for a matrix-model-like approach to three-dimensional quantum gravity. 2 When coupling many U(1)-fields, the authors in [12] found a promise of a phase transition higher than first order, which, however, is in conflict with the result in [13].3 As well, a certain minisuperspace model of GR can be derived from CTM [19].…”

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confidence: 99%

Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity

2017

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The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor of CTM up to the fourth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal symmetry, while the time evolution of the scale factor is power-law in dimensions below six.

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“…As for its relation to general relativity, the following properties have been shown. (i) In the simplest case 4 , CTM classically agrees with the mini-superspace approximation of general relativity [20]. (ii) In a formal continuum limit with N → ∞, the algebraic structure of the constraints of CTM agrees with that of the ADM formalism [21].…”

Section: Introductionmentioning

confidence: 74%

“…The familiar notation would be more appropriate, because the conjugate pair appears symmetrically in the new formulation. 6 In [20], this parameter plays the role of the cosmological constant in the mini-superspace approximation of general relativity. where t is a time variable.…”

Section: Review Of Ctmmentioning

confidence: 99%

Mother canonical tensor model

Narain

Sasakura

2017

Class. Quantum Grav.

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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.

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Interpreting canonical tensor model in minisuperspace

Cited by 30 publications

References 38 publications

Emergent symmetries in the canonical tensor model

Emergent symmetries in the canonical tensor model

Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity

Mother canonical tensor model

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