Progress in the numerical studies of the type IIB matrix model

Abstract

The type IIB matrix model, also known as the IKKT model, has been proposed as a promising candidate for a non-perturbative formulation of superstring theory. Based on this proposal, various attempts have been made to explain how our four-dimensional space-time can emerge dynamically from superstring theory. In this article, we review the progress in numerical studies on the type IIB matrix model. We particularly focus on the most recent results for the Euclidean and Lorentzian versions, which are obtained using the complex Langevin method to overcome the sign problem. We also review the earlier results obtained using conventional Monte Carlo methods and clarify the relationship among different calculations.

arXiv comment23 pages, contribution to the EPJ ST Special Issue: Noncommutativity and Physics, see https://www.epj.org/open-calls-for-papers/85-epj-st/2280-epjst-special-issue-noncommutativity-and-physics

References in corpus (52)

• A Large-N Reduced Model as Superstring
• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The Complex Langevin method: When can it be trusted?
• Space-Time Structures from IIB Matrix Model
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Monte Carlo Approach to M-Theory
• Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Dynamical Aspects of Large N Reduced Models
• The argument for justification of the complex Langevin method and the condition for correct convergence
• IIB Matrix Model
• Monte Carlo Studies of the IIB Matrix Model at Large N
• New insights into the problem with a singular drift term in the complex Langevin method
• A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
• Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory
• The RHMC Algorithm for 2 Flavours of Dynamical Staggered Fermions
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Convergent Yang-Mills Matrix Theories
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• String Field Theory from IIB Matrix Model
• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Brane world from IIB matrices
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory
• New proposal for numerical simulations of theta-vacuum like systems
• Justification of the complex Langevin method with the gauge cooling procedure
• Late time behaviors of the expanding universe in the IIB matrix model
• On the propagation across the big bounce in an open quantum FLRW cosmology
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Emergent Cosmology from Matrix Theory
• Gravity as a Quantum Effect on Quantum Space-Time
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Dynamical stabilisation of complex Langevin simulations of QCD
• A general approach to the sign problem - the factorization method with multiple observables
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• Emergent Metric Space-Time from Matrix Theory
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• Cosmic time evolution and propagator from a Yang-Mills matrix model
• A practical solution to the sign problem in a matrix model for dynamical compactification
• Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• The Area Law in Matrix Models for Large N QCD Strings
• Complex Langevin studies of the emergent space-time in the type IIB matrix model
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• IIB matrix model and regularized big bang
• Lattice Superstring and Noncommutative Geometry
• Recent developments in the type IIB matrix model

Cited by in corpus (8)

• One-loop effective action of the IKKT model for cosmological backgrounds
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Regularization of matrices in the covariant derivative interpretation of matrix models
• Quantisation of type IIB superstring theory and the matrix model
• The dynamics of zero modes in lattice gauge theory -- difference between SU(2) and SU(3) in 4D
• Fuzzy Black Holes from Mass Generation in Matrix Compactification
• Collective field theory of gauged multi-matrix models: Integrating out off-diagonal strings
• Twisting BFSS & IKKT