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

• Chen, Hua

  Yukawa Institute for Theoretical Physics, Kyoto University

• Sasakura, Naoki

  Yukawa Institute for Theoretical Physics, Kyoto University

• Sato, Yuki

  Department of Physics, Faculty of Science, Chulalongkorn University

Abstract

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 Arnowitt-Deser-Misner formalism of general relativity, and it 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 we 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 a power law in dimensions below six.

Journal

• Physical Review D

  Physical Review D 95 (6), 2017-03-15

  American Physical Society (APS)

Details

• CRID: 1050565162988431744
• NII Article ID: 120006822580
• ISSN: 24700010
• HANDLE: 2433/250153
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles