M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory

Abstract

A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to underlie all superstring theories. This is the only candidate at present for a theory of fundamental physics which reconciles gravity and quantum field theory in a potentially realistic fashion. Evidence for the existence of M-theory is still only circumstantial---no complete background-independent formulation of the theory yet exists. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, the theory appeared in a different guise as the discrete light-cone quantization of M-theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory which reduces to a supersymmetric theory of gravity at low energies. Although the fundamental degrees of freedom of matrix theory are essentially pointlike, it is shown that higher-dimensional fluctuating objects (branes) arise through the nonabelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed.

56 pages, 3 figures, LaTeX, revtex style; v2: references added

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• A Matrix Model for Heterotic $Spin(32)/Z_2$ and Type I String Theory
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• On the supersymmetric formulation of Unitary Matrix Model of type IIB
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• The Discrete Bound State Spectrum of the Rotating D0-brane System
• M-Branes and Their Interactions in Static Matrix Model
• Probing D0-D6 Black Hole Configuration: 2-Loop Matrix Theory Correction to D0-Brane Effective Action

Cited by in corpus (215)

• Noncommutative Field Theory
• Matrix Perturbation Theory For M-theory On a PP-Wave
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Nonperturbative aspects of ABJM theory
• Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space
• A Matrix Big Bang
• Transverse Fivebranes in Matrix Theory
• Three-dimensional N=6 SCFT's and their membrane dynamics
• Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture
• Non-abelian Brane Intersections
• D-branes and K-theory in 2D topological field theory
• Convergent Yang-Mills Matrix Theories
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
• Time-dependent AdS/CFT Duality and Null Singularity
• Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory
• Supermembrane on the PP-wave Background
• Monte Carlo studies of Matrix theory correlation functions
• Giant Hedge-Hogs: Spikes on Giant Gravitons
• Non-abelian Action for Multiple Five-Branes with Self-Dual Tensors
• The Black Hole S-Matrix from Quantum Mechanics
• Black hole entropy from non-perturbative gauge theory
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Probing black holes in non-perturbative gauge theory
• Branes from Matrix Theory in PP-Wave Background
• Matrix embeddings on flat $R^3$ and the geometry of membranes
• Emergent Spacetime and The Origin of Gravity
• Time and M-theory
• Background Independent Quantum Mechanics and Gravity
• Emergent Cosmology from Matrix Theory
• High precision study of the structure of D=4 supersymmetric Yang-Mills quantum mechanics
• Chaos in Matrix Models and Black Hole Evaporation
• Aspects of supertubes
• Matrix Cosmology
• Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk Metric and Possible Resolution of Singularity
• Noncommutative gravity: fuzzy sphere and others
• Five-Brane Thermodynamics from the Matrix Model
• Notes on Matrix Models
• Effective action and phase transitions of scalar field on the fuzzy sphere
• Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Super-Group Field Cosmology
• Membrane topology and matrix regularization
• Emergent Geometry and Quantum Gravity
• de Sitter entropy from conformal field theory
• The shape of nonabelian D-branes
• Exact Witten Index in D=2 supersymmetric Yang-Mills quantum mechanics
• Fuzzy spaces and new random matrix ensembles
• Energy-momentum Tensors in Matrix Theory and in Noncommutative Gauge Theories
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• String states, loops and effective actions in noncommutative field theory and matrix models
• Zero-Branes, Quantum Mechanics and the Cosmological Constant
• Bulk Entanglement Entropy and Matrices
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Worldsheet Formalism for Decoupling Limits in String Theory
• Superfield theory and supermatrix model
• Noncommutative Electromagnetism As A Large N Gauge Theory
• Review of Lattice Supersymmetry and Gauge-Gravity Duality
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Marginal Deformations In the Open Bosonic String Field Theory for N D0-branes
• Matrix dynamics of fuzzy spheres
• Recombination of Intersecting D-branes in Tachyon Field Theory
• An extended standard model and its Higgs geometry from the matrix model
• Matrix Theory Reloaded: A BPS Road to Holography
• Relating branes and matrices
• Mini-BFSS in Silico
• Nearing 11d Extremal Intersecting Giants and New Decoupled Sectors in D = 3,6 SCFT's
• A Thermodynamic Interpretation of Time for Rolling Tachyons
• The heat kernel of the compactified D=11 supermembrane with non-trivial winding
• Non-Commutative Geometry from Strings
• Non-Lorentzian IIB Supergravity from a Polynomial Realization of SL(2,R)
• Quantum Gravity from Noncommutative Spacetime
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Construction of the Zero-Energy State of SU(2)-Matrix Theory: Near the Origin
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Non-perturbative states in type II superstring theory from classical spinning membranes
• Warm p-soup and near extremal black holes
• Dynamical tachyons on fuzzy spheres
• Quantization of Emergent Gravity
• On the transverse M5-branes in matrix theory
• Graded Hopf Maps and Fuzzy Superspheres
• Matrix strings in a B-field
• (Non)Commutative Finsler Geometry from String/M--theory
• Random matrix approach to scalar fields on fuzzy spaces
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Yang-Mills Matrix Theory
• Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds
• Exact microscopic wave function for a topological quantum membrane
• Membrane and Noncommutativity
• Euler Top Dynamics of Nambu-Goto P-Branes
• Bosonic p-brane and A--D--M decomposition
• Matrix string theory, contact terms, and superstring field theory
• 11D supergravity at $\mathcal{O}(l^3)$
• Expanded Strings in the Background of NS5-branes via a M2-brane, a D2-brane and D0-branes
• Supersymmetric Yang-Mills quantum mechanics in various dimensions
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory
• Nilpotent Symmetries in Super-Group Field Cosmology
• On the SO(9) structure of supersymmetric Yang-Mills quantum mechanics
• Rotating Toroidal Branes in Supermembrane and Matrix Theory
• On Classification Of The Bubbling Geometries
• On D0 brane polarization by tidal forces
• Interpolating Action for Strings and Membranes - a Study of Symmetries in the Constrained Hamiltonian Approach
• Supergravity, Supermembrane and M(atrix) model on PP-Waves
• Emergence of $R^4$-terms in M-theory
• Supermatrix models for M-theory based on osp(1|32,R)
• Membranes from monopole operators in ABJM theory: large angular momentum and M-theoretic AdS_4/CFT_3
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• On a Matrix Model of Level Structure
• A Thermodynamic Interpretation of Time for Superstring Rolling Tachyons
• Electrified BPS Giants: BPS configurations on Giant Gravitons with Static Electric Field
• Matrix Model Thermodynamics
• On quantum mechanics as constrained N=2 supersymmetric classical mechanics
• An Introduction to the Quantum Supermembrane
• Loop formulation of supersymmetric Yang-Mills quantum mechanics
• Exact solutions for U(1) globally invariant membranes
• Random volumes from matrices
• A New String in Ten Dimensions?
• The arithmetic geometry of AdS${}_2$ and its continuum limit
• The number of gauge singlets in supersymmetric Yang-Mills quantum mechanics
• Spherical transverse M5-branes from the plane wave matrix model
• Quadrupole Instabilities of Relativistic Rotating Membranes
• Thermofield dynamics and Gravity
• Wave Packets in Discrete Quantum Phase Space
• Quantum gravity equation in large N Yang-Mills quantum mechanics
• Stringy Membranes in AdS/CFT
• Quiver Matrix Mechanics for IIB String Theory (I): Wrapping Membranes and Emergent Dimension
• PP-Wave Strings from Membrane and from String in the Spacetime with Two Time Directions
• Metastring Theory and Modular Space-time
• Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects
• Quantum Cellular Automata from Lattice Field Theories
• Penrose limit and DLCQ of string theory
• Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?
• Fuzzy spheres from inequivalent coherent states quantizations
• Strings in the pp-wave Background from Membrane
• On membrane interactions and a three-dimensional analog of Riemann surfaces
• BUSSTEPP Lectures on String Theory
• D0 Matrix Mechanics: New Fuzzy Solutions at Large N
• The Background Field Method for N = 2, d3 Super Chern-Simons-Matter Theories
• Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
• Emergent Spacetime for Quantum Gravity
• Covariantized Matrix theory for D-particles
• On Tachyon Condensation of Intersecting Noncommutative Branes in M(atrix) Theory
• Open and Winding Membranes, Affine Matrix Theory and Matrix String Theory
• Equilibration of Small and Large Subsystems in Field Theories and Matrix Models
• DLCQ strings and branched covers of torii
• On The Interaction Of D0-Brane Bound States And RR Photons
• N D0-branes and antibranes in the background independent string field theory
• Fully Off-shell Effective Action and its Supersymmetry in Matrix Theory II
• Non-Supersymmetric String Theory
• Matrix Theory for the DLCQ of Type IIB String Theory on the AdS/Plane-wave
• Renormalization of Supersymmetric Lifshitz Sigma Models
• Matrix Effective Theories of the Fractional Quantum Hall effect
• On the Ground State Wave Function of Matrix Theory
• Jordan Algebras and Extremal Black Holes
• Quiver Matrix Mechanics for IIB String Theory (II): Generic Dual Tori, Fractional Matrix Membrane and $SL(2,\integer)$ Duality
• Renormalizability of Supersymmetric Group Field Cosmology
• Black Hole and Fuzzy Objects in BFSS Matrix Model
• Noncritical M-theory: Three Dimensions
• Graviton and Spherical Graviton Potentials in Plane-Wave Matrix Model - overview and perspective -
• Emergent Spacetime and Cosmic Inflation
• DLCQ Strings, Twist Fields and One-Loop Correlators on a Permutation Orbifold
• Bulk Witten Indices from D=10 Yang Mills Integrals
• Membrane scattering from Bagger-Lambert theory
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• Uniqueness of the coordinate independent Spin(9)xSU(2) state of Matrix Theory
• The Autodidactic Universe
• Matrix Orientifolding and Models with Four or Eight Supercharges
• Emergent spacetime & Quantum Entanglement in Matrix theory
• Little IIB Matrix Model
• Nonperturbative Formulations of Superstring Theory
• Strings in pp-wave background and background B-field from membrane and its symplectic quantization
• Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics: S-Matrix and Metastable States
• Five-dimensional SYM from undeformed ABJM
• Spin(9) Average of SU(N) Matrix Models I. Hamiltonian
• Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• Decoding the matrix: Coincident membranes on the plane wave
• Bloch Waves and Fuzzy Cylinders: 1/4-BPS Solutions of Matrix Theory
• Mass-Gaps and Spin Chains for (Super) Membranes
• Remark about string field for general configuration of N D-instantons
• On Strongly Coupled Matrix Theory and Stochastic Quantization: A New Approach to Holographic Dualities
• Entanglement Entropy for the Black 0-Brane
• D=4 supersymmetric Yang-Mills quantum mechanics with three colors
• Diffeomorphism Algebra Structure and Membrane Theory
• Modeling M-Theory Vacua via Gauged S-Duality
• Eigenvalues and eigenvectors of the Laplace operator in d-dimensional cut Fock basis
• Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra
• Emergence of longitudinal 7-branes and fuzzy S^4 in compactification scenarios of M(atrix) theory
• The SU(N) Matrix Model at Two Loops
• Gravitation with Two Times
• Comment on Counting Black Hole Microstates Using String Dualities
• Global unitary fixing and matrix-valued correlations in matrix models
• Orientifolded Matrices and Supersymmetries that Give Rise to Spacetime Directional Asymmetry of Effective Interactions
• The AdS/CFT Correspondence: Classical, Quantum, and Thermodynamical Aspects
• Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background
• Thermal Lie Superalgebras
• String Theory, Large Dimensions and Supersymmetry
• Dynamical Aspects on Duality between SYM and NCOS from D2-F1 Bound State
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models
• Aspects of noncommutativity in field theory, strings and membranes
• Matrix Model for membrane and dynamics of D-Particles in a curved space-time geometry and presence of form fields
• Two-Graviton Interaction in PP-Wave Background in Matrix Theory and Supergravity
• Solutions of the generalized Weierstrass representation in four-dimensional Euclidean space
• Effects of Matrix Orientifolding to Two-Loop Effective Action of Bosonic IIB Matrix Model
• Time-dependent Backgrounds in String Theory and Dualities
• Apparent Geometry from the Quantum Mechanics of $Sp(8,\mathbb{C})$
• Time and a Temporally Statistical Quantum Geometrodynamics
• Zero-mode Spectrum of Eleven-dimensional Theory on the Plane-wave Background
• Twisting BFSS & IKKT
• Collective field theory of gauged multi-matrix models: Integrating out off-diagonal strings
• On Emergent Geometry from Entanglement Entropy in Matrix theory
• On matrix description of D-branes
• Gauge Field on Brane in M-atrix Theory