A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Abstract

Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this `complex-action problem', which utilizes a factorization property of distribution functions. The basic idea is quite general, and it removes the so-called overlap problem completely. Here we apply the method to a nonperturbative study of superstring theory using its matrix formulation. In this particular example, the distribution function turns out to be positive definite, which allows us to reduce the problem even further. Our numerical results suggest an intuitive explanation for the dynamical generation of 4d space-time.

7 pages, 4 figures, PRD version somewhat extended from the original version

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Cited by in corpus (75)

• The phase diagram of dense QCD
• High density QCD on a Lefschetz thimble?
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• The QCD phase diagram at nonzero quark density
• Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• The density of states method at non-zero chemical potential
• Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• On the existence of the critical point in finite density lattice QCD
• Easing the Monte Carlo sign problem
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory
• Effective Actions of Matrix Models on Homogeneous Spaces
• The fermion determinant in (4,4) 2d lattice super-Yang-Mills
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Emergent Cosmology from Matrix Theory
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Histograms in heavy-quark QCD at finite temperature and density
• Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time
• Stability of fuzzy $S^2\times S^2$ geometry in IIB matrix model
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Supersymetry on the Noncommutative Lattice
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• A general approach to the sign problem - the factorization method with multiple observables
• Progress in the numerical studies of the type IIB matrix model
• Perturbative dynamics of fuzzy spheres at large N
• Distributions of the Phase Angle of the Fermion Determinant in QCD
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Evading the sign problem in random matrix simulations
• Dynamical aspects of the plane-wave matrix model at finite temperature
• 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
• Phase structure of hot dense QCD by a histogram method
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Applying constrained simulations for low temperature lattice QCD at finite baryon chemical potential
• Theta-vacuum systems via real action simulations
• The density in the density of states method
• N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• Fuzzy Torus in Matrix Model
• Monte Carlo Studies of the GWW Phase Transition in Large-N Gauge Theories
• Improved Perturbation Method and its Application to the IIB Matrix Model
• Free energy of the self-interacting relativistic lattice Bose gas at finite density
• Testing the Gaussian expansion method in exactly solvable matrix models
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Existence of positive representations for complex weights
• Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
• The sign problem across the QCD phase transition
• Holographic realization of large-Nc orbifold equivalence with non-zero chemical potential
• Adding a Myers Term to the IIB Matrix Model
• A subset solution to the sign problem in random matrix simulations
• Sampling scheme for neuromorphic simulation of entangled quantum systems
• The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• Effective Actions of IIB Matrix Model on S^3
• Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
• The Fluctuations of the Quark Number and of the Chiral Condensate
• The instability of intersecting fuzzy spheres
• Lattice Superstring and Noncommutative Geometry
• The density of states approach for the simulation of finite density quantum field theories
• Putting M theory on a computer
• Little IIB Matrix Model
• (3+1)-dimensional expanding universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• Sampling and the complexity of nature
• The density of states approach to the sign problem
• On the validity of complex Langevin method for path integral computations
• Recent developments in the type IIB matrix model
• The Factorization Method for Monte Carlo Simulations of Systems With a Complex Action
• Taming the pion condensation in QCD at finite baryon density
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking