Dynamical Aspects of Large N Reduced Models

Abstract

We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N by N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually saturated. The relation of our result to the SSB of the U(1)^D symmetry in the Eguchi-Kawai model is clarified. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of space time, which means that a classical space-time picture is maximally broken. We develop a 1/D expansion, which enables us to calculate correlation functions of the model analytically. The absence of an SSB of the Lorentz invariance is shown by the Monte Carlo simulation as well as by the 1/D expansion.

41 pages, LaTeX, 15 eps figures; comments added for the well-definedness of the models and for a related reference

References in corpus (3)

• Space-Time Structures from IIB Matrix Model
• Finite Yang-Mills Integrals
• Numerical Study of the Double Scaling Limit in Two-Dimensional Large N Reduced Model

Cited by in corpus (104)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Convergent Yang-Mills Matrix Theories
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• The Phase Structure of Low Dimensional Large N Gauge Theories on Tori
• The BFSS model on the lattice
• Brane world from IIB matrices
• Extracting black hole physics from the lattice
• Multi-matrix models and emergent geometry
• Phases of one dimensional large N gauge theory in a 1/D expansion
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Eigenvalue Distributions in Yang-Mills Integrals
• Phase structure of matrix quantum mechanics at finite temperature
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Late time behaviors of the expanding universe in the IIB matrix model
• Testing holography using lattice super-Yang--Mills on a 2-torus
• Exactly Solvable Matrix Models for the Dynamical Generation of Space-Time in Superstring Theory
• Yang-Mills Integrals for Orthogonal, Symplectic and Exceptional Groups
• Supermatrix Models
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Emergent Cosmology from Matrix Theory
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• High temperature expansion in supersymmetric matrix quantum mechanics
• Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Matrix Geometry and Coherent States
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities
• On the shape of a D-brane bound state and its topology change
• Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
• More on the New Large $D$ Limit of Matrix Models
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Progress in the numerical studies of the type IIB matrix model
• Perturbative dynamics of fuzzy spheres at large N
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
• Emergent Metric Space-Time from Matrix Theory
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Phases of a two dimensional large N gauge theory on a torus
• Large N limit of the IKKT matrix model
• Lectures on Matrix Field Theory I
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
• Cascade of Gregory-Laflamme Transitions and U(1) Breakdown in Super Yang-Mills
• Rotational Symmetry Breaking in Multi-Matrix Models
• Bulk geometry in gauge/gravity duality and color degrees of freedom
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals
• Nonabelian Monopoles from Matrices: Seeds of the Spacetime Structure
• Matrix geometries and Matrix Models
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Warm p-soup and near extremal black holes
• Local field theory from the expanding universe at late times in the IIB matrix model
• Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model
• Yang-Mills Matrix Theory
• On the Phase Structure of Commuting Matrix Models
• Testing the Gaussian expansion method in exactly solvable matrix models
• Near commuting multi-matrix models
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• Nuclear states and spectra in holographic QCD
• Yang-Mills Integrals
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• A practical solution to the sign problem in a matrix model for dynamical compactification
• The Area Law in Matrix Models for Large N QCD Strings
• On the supersymmetric formulation of Unitary Matrix Model of type IIB
• Matrix models and the gravitational interaction
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• New States of Gauge Theories on a Circle
• The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --
• Large N Reductions and Holography
• Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• Simulating Simplified Versions of the IKKT Matrix Model
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• Introduction to Monte Carlo for Matrix Models
• Polyakov Lines in Yang-Mills Matrix Models
• Nucleus from String Theory
• Phase structure of the large-N reduced gauge theory and generalized Weingarten model
• Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
• Yang-Mills Integrals
• Lattice Superstring and Noncommutative Geometry
• Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
• The instability of intersecting fuzzy spheres
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Two approaches to quantum gravity and M-(atrix) theory at large number of dimensions
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• (3+1)-dimensional expanding universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• On the Quantum Geometry of String Theory
• Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
• High-Precision Bootstrap of Multimatrix Quantum Mechanics
• Note on a Closed String Field Theory from Bosonic IIB Matrix Model
• Monte Carlo Simulations of BFSS and IKKT Matrix Models
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking
• Optimized Fock space in the large N limit of quartic interactions in Matrix Models
• Effects of Matrix Orientifolding to Two-Loop Effective Action of Bosonic IIB Matrix Model
• Randomized Wilson loops, reduced models and the large D expansion