arXiv subjects

Hiroshi Kawabe

Publications and source records attributed to Hiroshi Kawabe.

6 recordsLinked to original sources

arXiv2021

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

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.

hep-th↗

arXiv2016

Causal dynamical triangulation of a 3D tensor model

We extend the string field theory of 2D generalized causal dynamical triangulation (GCDT) with the Ishibashi-Kawai type (IK-type) interaction formulated by the matrix model to the 3D model of the surface field theory. Based on the loop gas model, we construct a tensor model for the discretized surface field and then apply it the stochastic quantization method. In the double-scaling limit, the model is characterized by two scaling dimensions $D$ and $D_N$, the power indices of the minimal length as the scaling parameter. The continuum GCDT model with the IK-type interaction is realized with a similar restriction in the $D_N$-$D$ space to the 2D model. The distinct property in the 3D model is that the quantum effect contains the IK-type interaction only, while the ordinary splitting interaction is excluded.

hep-th↗

arXiv2013

Causal dynamical triangulation for non-critical open-closed string field theory

We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from the usual model of closed string to the one of open-closed string. The matrix-vector model describing the loop gas model is modified so as to possess the nature of the CDT, i.e. the time foliation structure. Stochastic quantization method produces interactions of loop and line variables similar to those in the non-critical open-closed string field theories. By taking an appropriate scaling, we realize an extended model of the generalized CDT (GCDT), which keeps the causality in a broad sense.

hep-th↗

arXiv2013

Stochastic Quantization Approach for Causal Dynamical Triangulation String Field Theory

We construct a 2-dimensional Causal Dynamical Triangulation (CDT) model from a matrix model which represents the loop gas model of closed string. The target-space index is reinterpreted as time or geodesic distance. We apply stochastic quantization method to the model to obtain the Generalized CDT (GCDT), which has additional interaction of creating baby universe. If we take a specific scaling in continuum limit, we realize an extended GCDT model characterized by the non-critical string field theory.

hep-th↗

arXiv2002

Note on a Closed String Field Theory from Bosonic IIB Matrix Model

We apply stochastic quantization method to the bosonic part of IIB matrix model, i.e., a naive zero volume limit of large N Yang-Mills theory, to construct a collective field theory of Wilson loops. The Langevin equation for Wilson loops can be interpreted as the time evolution of closed string fields. The corresponding Fokker-Planck hamiltonian deduces a closed string field theory which describes interacting Wilson loops with manifest Lorentz invariance.

hep-th↗

arXiv1999

Algebraic Structure in 0<c<1 Open-Closed String Field Theories

We apply stochastic quantization method to Kostov's matrix-vector models for the second quantization of orientable strings with Chan-Paton like factors, including both open and closed strings. The Fokker-Planck hamiltonian deduces an orientable open-closed string field theory at the double scaling limit. There appears an algebraic structure in the continuum F-P hamiltonian including a Virasoro algebra and a SU(r) current algebra.

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