IIB Matrix Model

Abstract

We review our proposal for a constructive definition of superstring, type IIB matrix model. The IIB matrix model is a manifestly covariant model for space-time and matter which possesses N=2 supersymmetry in ten dimensions. We refine our arguments to reproduce string perturbation theory based on the loop equations. We emphasize that the space-time is dynamically determined from the eigenvalue distributions of the matrices. We also explain how matter, gauge fields and gravitation appear as fluctuations around dynamically determined space-time.

37 pages, LaTex with PTPTex.sty, 2 epsf figures. Proceedings of the 13th Nishinomiya Yukawa Memorial Symposium (November, 1998)

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• Noncommutative Yang-Mills in IIB Matrix Model
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Introduction to M(atrix) theory and noncommutative geometry
• Wilson Loops in Noncommutative Yang Mills
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Monte Carlo Studies of the IIB Matrix Model at Large N
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• Mean Field Approximation of IIB Matrix Model and Emergence of Four Dimensional Space-Time
• Convergent Yang-Mills Matrix Theories
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• D-branes, Matrix Theory and K-homology
• Improved Perturbation Theory and Four-Dimensional Space-Time in IIB Matrix Model
• Bi-local Fields in Noncommutative Field Theory
• 6D Fractional Quantum Hall Effect
• Spectra of supersymmetric Yang-Mills quantum mechanics
• String Scale in Noncommutative Yang-Mills
• Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
• Supermatrix Models
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Dynamical generation of a nontrivial index on the fuzzy 2-sphere
• Matrix Model Approach to Cosmology
• On Higher Dimensional Fuzzy Spherical Branes
• Chiral Anomaly on Fuzzy 2-Sphere
• A general approach to the sign problem - the factorization method with multiple observables
• Progress in the numerical studies of the type IIB matrix model
• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
• Perturbative dynamics of fuzzy spheres at large N
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Orbifold Matrix Model
• Stability of the fuzzy sphere solution from matrix model
• Rotational Symmetry Breaking in Multi-Matrix Models
• Matrix Model Cosmology in Two Space-time Dimensions
• N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
• Quantum (Matrix) Geometry and Quasi-Coherent States
• Interaction between two Fuzzy Spheres
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Curved-space classical solutions of a massive supermatrix model
• Lie 2-algebra models
• Fuzzy Torus in Matrix Model
• M-theory and the birth of the Universe
• Yang-Mills Matrix Theory
• $L_{\infty }$-Algebra Models and Higher Chern-Simons Theories
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• Perturbative Vacua from IIB Matrix Model
• A practical solution to the sign problem in a matrix model for dynamical compactification
• Supercurrent Interactions in Noncommutative Yang-Mills and IIB Matrix Model
• Big bang as a topological quantum phase transition
• The Area Law in Matrix Models for Large N QCD Strings
• DDF and Pohlmeyer invariants of (super)string
• Matrix models and the gravitational interaction
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Nonabelian 2-forms and loop space connections from SCFT deformations
• Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2
• Probability of the Standard Model Appearance from a Matrix Model
• IIB matrix model and regularized big bang
• Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Noncommutative Static Strings from Matrix Models
• Emergent gravity from the IIB matrix model and cancellation of a cosmological constant
• A note on higher spin symmetry in the IIB matrix model with the operator interpretation
• Numerical Analysis of the Double Scaling Limit in the IIB Matrix Model
• A note on graviton exchange in emergent gravity scenario
• Effective Actions of IIB Matrix Model on S^3
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Projectors, matrix models and noncommutative monopoles
• Matrix model with manifest general coordinate invariance
• A first look at the bosonic master-field equation of the IIB matrix model
• Yang-Mills Integrals
• A Proposal for a Non-Perturbative Regularization of {\cal N}=2 SUSY 4D Gauge Theory
• Probability distribution over some phenomenological models in the matrix model compactified on a torus
• Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• Axial anomaly in the reduced model: Higher representations
• IIB Matrix Model with D1-D5 Backgrounds
• Lattice Superstring and Noncommutative Geometry
• IIB matrix model: Extracting the spacetime metric
• Numerical Analysis of the Double Scaling Limit in the bosonic part of the IIB Matrix Model
• Categorical Perspective on Quantization of Poisson Algebra
• Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere
• Large-N behaviors of the IIB matrix model and the regularized Schild models
• Scaling Behaviors of Branched Polymers
• Matrix Model and Ginsparg-Wilson Relation
• Stability of the Matrix Model in Operator Interpretation
• Little IIB Matrix Model
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Super Yang-Mills theory in 10+2 dimensions, The 2T-physics Source for N=4 SYM and M(atrix) Theory
• IIB matrix model: Emergent spacetime from the master field
• Note on a Closed String Field Theory from Bosonic IIB Matrix Model
• Emergence of longitudinal 7-branes and fuzzy S^4 in compactification scenarios of M(atrix) theory
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
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• Regularized big bang singularity: Geodesic congruences
• Twisting BFSS & IKKT
• Replicas, averaging and factorization in the IIB matrix model
• On the emergence of an expanding universe from a Lorentzian matrix model
• Phenomenological studies in the matrix models
• U(2) projectors and 't Hooft-Polyakov monopoles on a fuzzy sphere