arXiv subjects

Matsuo Sato

Publications and source records attributed to Matsuo Sato.

At least 19 recordsLinked to original sources

arXiv2026

Mutation and crossover of simplicial complexes

Color graphs and their subgraphs, referred to as bubble graphs, correspond bijectively to the simplicial complexes of pseudomanifolds and their subsimplices, respectively. In this paper, we introduce matrix representations for colored graphs and their associated bubble graphs. By using this correspondence, we define simplicial-complex matrices and subsimplex matrices that encode the simplicial complexes of pseudomanifolds and their subsimplices. Moreover, we formulate mutation and crossover operations on colored graphs. Through the established correspondence among simplicial complexes, colored graphs, and simplicial-complex matrices, we extend these operations to simplicial complexes and simplicial-complex matrices. We further implement an algorithm generating simplicial-complex matrices and a genetic algorithm performing mutation and crossover of them to produce pseudomanifolds exhibiting diverse topologies. In addition, we implement procedures for decomposing the generated simplicial-complex matrices into simplex matrices, reconstructing the simplicial complexes of the associated pseudomanifolds from this information, and computing geometric quantities such as the volume, circumcenter, and dual-simplex volume of each simplex.

hep-th↗

arXiv2025

The perturbative vacua in string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, in the bosonic closed sector of string geometry theory, we completely identify the perturbative vacua, which include general string backgrounds in bosonic closed string theory. From fluctuations around these configurations, we derive the path-integrals of perturbative strings on the string backgrounds up to any order.

hep-th↗

arXiv2025

String geometry phenomenology

Recently, a potential for string backgrounds is obtained from string geometry theory, which is a candidate for the non-perturbative formulation of string theory. By substituting a string phenomenological model with free parameters to the potential, one obtains a potential for the free parameters, whose minimum determines the free parameters. The model with the determined parameters is the ground state in the model. This will be the local minimum in a partial region of the model in the string theory landscape. By comparing it with the other local minimum, one can determine which model is near the minimum of the potential for string backgrounds, that will be the true vacuum in string theory, in the sense of the values of the potential. We will be able to find the true vacuum in string theory through a series of such researches. In this paper, we perform this analysis of a certain simple heterotic non-supersymmetric model explicitly, where the six-dimensional internal spaces are products of two-dimensional spaces of constant curvatures, and the generation number of massless fermions is given by the flux quantization numbers. As a result, we obtain a constraint between the compactification scale and the flux quanta.

hep-th↗

arXiv2025

The heterotic perturbative vacua in string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of superstring theory. In this paper, in string geometry theory, we identify perturbative heterotic vacua, which include general heterotic backgrounds. From fluctuations around these vacua, we derive the path-integrals of heterotic perturbative superstrings on the backgrounds up to any order.

hep-th↗

arXiv2025

Fundamental structure of string geometry theory

String geometry theory is one of the candidates of a non-perturbative formulation of string theory. In this theory, the ``classical'' action is almost uniquely determined by T-symmetry, which is a generalization of the T-duality, where the parameter of ``quantum'' corrections $β$ in the path-integral of the theory is independent of that of quantum corrections $\hbar$ in the perturbative string theories. We distinguish the effects of $β$ and $\hbar$ by putting " " like "classical" and "loops" for tree level and loop corrections with respect to $β$, respectively, whereas by putting nothing like classical and loops for tree level and loop corrections with respect to $\hbar$, respectively. A non-renormalization theorem states that there is no ``loop'' correction. Thus, there is no problem of non-renormalizability, although the theory is defined by the path-integral over the fields including a metric on string geometry. No ``loop'' correction is also the reason why the complete path-integrals of the all-order perturbative strings in general string backgrounds are derived from the ``tree''-level two-point correlation functions in the perturbative vacua, although string geometry includes information of genera of the world-sheets of the stings. Furthermore, a non-perturbative correction in string coupling with the order $e^{-1/g_s^2}$ is given by a transition amplitude representing a tunneling process between the semi-stable vacua in the ``classical'' potential by an ``instanton'' in the theory. From this effect, a generic initial state will reach the minimum of the potential.

hep-th↗

arXiv2024

T-symmetry in String Geometry Theory

String geometry theory is one of the candidates of non-perturbative formulation of string theory. In this paper, we have shown that dimensionally reduced string geometry theories have what we call T-symmetry. In case of the dimensional reduction in space-like directions, the T-symmetry transformation gives the T-dual transformation between the type IIA and IIB perturbative vacua. In case of the dimensional reduction in the direction of string geometry time $\barτ$, the T-symmetry transformation is independent of the T-dual transformation, and gives a symmetry that cannot be seen in the perturbative string theories.

hep-th↗

arXiv2024

String Geometry Theory and The String Vacuum

String geometry theory is a candidate of the non-perturvative formulation of string theory. In this theory, strings constitute not only particles but also the space-time. In this review, we identify perturbative vacua, and derive the path-integrals of all order perturbative strings on the corresponding string backgrounds by considering the fluctuations around the vacua. On the other hand, the most dominant part of the path-integral of string geometry theory is the zeroth order part in the fluctuation of the action, which is obtained by substituting the perturbative vacua to the action. This part is identified with the effective potential of the string backgrounds and obtained explicitly. The global minimum of the potential is the string vacuum. The urgent problem is to find the global minimum. We introduce both analytical and numerical methods to solve it.

hep-th↗

arXiv2024

Gauge invariant discretization of Chern-Simons couplings

We discretize Chern-Simons couplings in gauge invariant way. We obtain (p+q)-forms representing Chern-Simons couplings on (p + q)-simplexes from wedge products of p- and q-forms on p- and q-simplexes, respectively, where p- and q-simplexes form (p+q)-simplexes by having a common vertex. We show that the Chern-Simons couplings on simplicial complexes reduce to Chern-Simons couplings on the manifolds in a continuum limit. Moreover, we prove that a typical discretized Chern-Simons term that has the Chern-Simons coupling is gauge invariant.

hep-lat↗

arXiv2022

Path integrals of perturbative strings on curved backgrounds from string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the closed bosonic sector of string geometry theory, we derive path integrals of all order perturbative strings on all the string backgrounds, $G_{μν}(x)$, $B_{μν}(x)$, and $Φ(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.

hep-th↗

arXiv2022

Path-integrals of perturbative superstrings on curved backgrounds from string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In this paper, from the string geometry theory, we derive path-integrals of perturbative superstrings on all the string backgrounds, $G_{μν}(x)$ and $B_{μν}(x)$, by considering fluctuations around the string background configurations, which are parametrized by the string backgrounds.

hep-th↗

arXiv2021

Superstring Backgrounds in String Geometry

String geometry theory is a candidate of the non-perturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we show that all the type IIA, IIB, SO(32) type I, and SO(32) and $E_8 \times E_8$ heterotic superstring backgrounds are embedded in configurations of the fields of a single string geometry model. Especially, we show that the configurations satisfy the equations of motion of the string geometry model in $α' \to 0$ if and only if the embedded string backgrounds satisfy the equations of motion of the supergravities, respectively. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

hep-th↗

arXiv2021

String Backgrounds in String Geometry

String geometry theory is a candidate of the non-perturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how string backgrounds are described in string geometry theory. In this paper, we show that the string backgrounds are embedded in configurations of the fields of a string geometry model. Especially, we show that the configurations satisfy the equations of motion of the string geometry model if and only if the embedded string backgrounds satisfy their equations of motion. This means that classical dynamics of the string backgrounds are described as a part of classical dynamics in string geometry theory. Furthermore, we define an energy of the configurations in the string geometry model because they do not depend on the string geometry time. A string background can be determined by minimizing the energy.

hep-th↗

arXiv2021

String Geometry and Non-perturbative Formulation of String Theory

We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert action coupled with gauge fields, and formulate superstring theory non-perturbatively by summing over metrics and the gauge fields on the spaces of strings. This theory does not depend on backgrounds. The theory has a supersymmetry as a part of the diffeomorphisms symmetry on the superstring manifolds. We derive the all-order perturbative scattering amplitudes that possess the super moduli in type IIA, type IIB and SO(32) type I superstring theories from the single theory, by considering fluctuations around fixed backgrounds representing type IIA, type IIB and SO(32) type I perturbative vacua, respectively. The theory predicts that we can see a string if we microscopically observe not only a particle but also a point in the space-time. That is, this theory unifies particles and the space-time.

hep-th↗

arXiv2020

Perturbative string theory from Newtonian limit of string geometry theory

String geometry theory is one of the candidates of the non-perturbative formulation of string theory. In arXiv:1709.03506, the perturbative string theory is reproduced from a string geometry model coupled with a $u(1)$ gauge field on string manifolds. In this paper, we generalize this result and we show that the perturbative string theory is reproduced from any string geometry model by taking a Newtonian limit.

hep-th↗

arXiv2020

Topological String Geometry

Perturbative string amplitudes are correctly derived from the string geometry theory, which is one of the candidates of a non-perturbative formulation of string theory. In order to derive non-perturbative effects rather easily, we formulate topological string geometry theory. We derive the perturbative partition function of the topological string theory from fluctuations around a classical solution in the topological string geometry theory.

hep-th↗

arXiv2019

Quantum Theory of the Universe Based on Bayesian Probability

We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a Bayesian probability, which can define a probability of an event that occurs just once. As an example, by applying the quantum theory of the Universe to an action of a scalar field theory in the four dimensions as a toy model for the theory of the Universe, we explicitly obtain the probability of the Universe and the action of matters in the Universe.

physics.gen-ph↗

arXiv2019

Moduli Space in Homological Mirror Symmetry

We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the $A_{\infty}$ structure of the both models.

hep-th↗

arXiv2014

On the Structure Constants of Volume Preserving Diffeomorphism Algebra

Regularizing volume preserving diffeomorphism (VPD) is equivalent to a long standing problem, namely regularizing Nambu-Poisson bracket. In this paper, as a first step to regularizing VPD, we find general complete independent basis of VPD algebra. Especially, we find complete independent basis that give simple structure constants, where three area preserving diffeomorphism (APD) algebras are manifest. This implies that an algebra that regularizes VPD algebra should include three u(N) Lie algebras.

hep-th↗