Quantum mechanics

Theoretical physics

Linguistics

Supersymmetry

Philosophy

Ecology

Mathematical physics

Biology

Statistics

Materials science

Block matrix

Operating system

Eigenvalues and eigenvectors

Computer science

Pauli exclusion principle

Statistical physics

Sign (mathematics)

Matrix (chemical analysis)

Type (biology)

Physics

Mathematics

Mathematical analysis

Composite material

Superstring theory

Monte Carlo method

Space (punctuation)

Langevin equation

Journal of High Energy Physics

A bstract The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has been found recently, however, that the matrix configurations generated by the simulation is singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem has been attributed to the approximation used to avoid the sign problem in simulating the model. Here we investigate the model using the complex Langevin method to overcome the sign problem instead of using the approximation. Our results indicate a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior is kept intact.

Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model