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

• Sasakura, Naoki

• Sato, Yuki

Abstract

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

Journal

• Journal of High Energy Physics

  Journal of High Energy Physics 2015 109-, 2015-10

  Springer Berlin Heidelberg

Keywords

• Models of Quantum Gravity
• Non-Commutative Geometry

Details

• CRID: 1050845760762751872
• NII Article ID: 120005749948
• NII Book ID: AA1188279X
• ISSN: 10298479
• DOI: 10.1007/jhep10(2015)109
• HANDLE: 2433/210402
• Web Site: http://link.springer.com/content/pdf/10.1007/JHEP10(2015)109
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN