Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model

Abstract

The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory, in which spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-$N$ limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding space-time. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.

arXiv comment34 pages, 5 figures; (v2) reference added

References in corpus (95)

• A Large-N Reduced Model as Superstring
• High density QCD on a Lefschetz thimble?
• 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
• Simulating full QCD at nonzero density using the complex Langevin equation
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Monte Carlo Approach to M-Theory
• Lattice simulations of real-time quantum fields
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Gauge cooling in complex Langevin for QCD with heavy quarks
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Dynamical Aspects of Large N Reduced Models
• Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model
• Adaptive stepsize and instabilities in complex Langevin dynamics
• Stochastic quantization at finite chemical potential
• 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
• 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
• Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
• Convergent Yang-Mills Matrix Theories
• Simulating nonequilibrium quantum fields with stochastic quantization techniques
• Describing Curved Spaces by Matrices
• Real-time gauge theory simulations from stochastic quantization with optimized updating
• Complex Langevin dynamics and zeroes of the fermion determinant
• The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-
• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Brane world from IIB matrices
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Improved Perturbation Theory and Four-Dimensional Space-Time in IIB Matrix Model
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Approximations for strongly-coupled supersymmetric quantum mechanics
• Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Intersecting branes and a standard model realization in matrix models
• Orbifolds, fuzzy spheres and chiral fermions
• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• Justification of the complex Langevin method with the gauge cooling procedure
• Late time behaviors of the expanding universe in the IIB matrix model
• The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Quantized open FRW cosmology from Yang-Mills matrix models
• On the Spontaneous Breakdown of Lorentz Symmetry in Matrix Models of Superstrings
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Applying Complex Langevin Simulations to Lattice QCD at Finite Density
• Chiral Fermions and the Standard Model from the Matrix Model Compactified on a Torus
• Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time
• Emergent gravity on covariant quantum spaces in the IKKT model
• Matrix Model Approach to Cosmology
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Dynamical stabilisation of complex Langevin simulations of QCD
• Gauge cooling for the singular-drift problem in the complex Langevin method --a test in Random Matrix Theory for finite density QCD
• An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles
• Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals
• A general approach to the sign problem - the factorization method with multiple observables
• Cosmological space-times with resolved Big Bang in Yang-Mills matrix models
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• Gaussian and Mean Field Approximations for Reduced 4D Supersymmetric Yang-Mills Integral
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry
• Orbifold Matrix Model
• Signature change in matrix model solutions
• Testing the criterion for correct convergence in the complex Langevin method
• An extended standard model and its Higgs geometry from the matrix model
• Lorentzian Fuzzy Spheres
• Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals
• Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models
• Stability of 4-dimensional Space-time from IIB Matrix Model via Improved Mean Field Approximation
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• Local field theory from the expanding universe at late times in the IIB matrix model
• Modifying partition functions: a way to solve the sign problem
• Realizing three generations of the Standard Model fermions in the type IIB matrix model
• Realizing chiral fermions in the type IIB matrix model at finite N
• Complex Langevin Simulations of Zero-dimensional Supersymmetric Quantum Field Theories
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• Complex Langevin Dynamics in Large $N$ Unitary Matrix Models
• Testing the Gaussian expansion method in exactly solvable matrix models
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• Brane compactifications and 4-dimensional geometry in the IKKT model
• A practical solution to the sign problem in a matrix model for dynamical compactification
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• Fuzzy $C{P}^2$ Space-Times
• Probability of the Standard Model Appearance from a Matrix Model
• Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
• Scalar modes and the linearized Schwarzschild solution on a quantized FLRW space-time in Yang-Mills matrix models
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model
• Matrix model and Yukawa couplings on the noncommutative torus

Cited by in corpus (10)

• Progress in the numerical studies of the type IIB matrix model
• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations
• Quantum (Matrix) Geometry and Quasi-Coherent States
• Emergent gravity from the IIB matrix model and cancellation of a cosmological constant
• A first look at the bosonic master-field equation of the IIB matrix model
• Complex Langevin Dynamics and Supersymmetric Quantum Mechanics
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• Quantisation of type IIB superstring theory and the matrix model
• Collective field theory of gauged multi-matrix models: Integrating out off-diagonal strings
• Fuzzy Black Holes from Mass Generation in Matrix Compactification