CDT open-closed surface field theory of a 3D tensor-matrix model

Abstract

We construct a tensor-matrix model which describes 3-dimensional (3D) Causal Dynamical Triangulation (CDT) of open-closed surface. Though the usual splitting interaction of a surface is not derived from the stochastic quantization procedure, it provides another interaction of IK-type, which becomes the sole quantum correction. Through the double scaling limit, it realizes CDT open-closed surface field theory including the IK-type interactions in the same condition with the closed surface CDT model. Further, we investigate the commutation relations of the generators, for surfaces with the lowest numbers of boundary loops, in the Fokker-Planck (FP) Hamiltonian. The generators seem to close in their commutation relations in our 3D model, differently from the 2D model, where the algebraic structure was not exact when commutators contain the generator of the open string edge.

arXiv comment23pages, 22figures, comments added, published version

References in corpus (25)

• Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
• Dynamically Triangulating Lorentzian Quantum Gravity
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Non-perturbative 3d Lorentzian Quantum Gravity
• String Field Theory of Noncritical Strings
• Strings with Discrete Target Space
• String Field Theory of $c\le 1$ Noncritical Strings
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• A new continuum limit of matrix models
• Loop Gas Model for Open Strings
• Loop Space Hamiltonians And Field Theory Of Non-Critical Strings
• Stochastic quantization and the role of time in quantum gravity
• Renormalization of 3d quantum gravity from matrix models
• Collective field theory of the matrix-vector model
• LOOP SPACE HAMILTONIAN FOR $c\le 1$ OPEN STRINGS
• Field Theory of Open and Closed Strings with Discrete Target Space
• Quantization of Geometry
• Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions
• On Field Theories of Loops
• Algebraic Structure in Non-Orientable Open-Closed String Field Theories
• Temporal-gauge String Field with Open Strings
• Stochastic Quantization Approach for Causal Dynamical Triangulation String Field Theory
• Algebraic Structure in 0<c<1 Open-Closed String Field Theories
• Causal dynamical triangulation for non-critical open-closed string field theory
• Causal dynamical triangulation of a 3D tensor model