Complex Langevin studies of the emergent space-time in the type IIB matrix model

G. Parisi, ON COMPLEX PROBABILITIES, Phys. Lett. B

1983

Earlier work this paper cites.

J. R. Klauder, Coherent State Langevin Equations for Canonical Quantum Systems With Applications to the Quantized Hall Effect, Phys. Rev. A

1984

Earlier work this paper cites.

N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A Large N reduced model as superstring, Nucl. Phys. B

1997

Earlier work this paper cites.

J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, JHEP

2002

Earlier work this paper cites.

H. Kawai, S. Kawamoto, T. Kuroki, T. Matsuo and S. Shinohara, Mean field approximation of IIB matrix model and emergence of four-dimensional space-time, Nucl. Phys. B

2002

Earlier work this paper cites.

T. Aoyama and H. Kawai, Higher order terms of improved mean field approximation for IIB matrix model and emergence of four-dimensional space-time, Prog. Theor. Phys

2006

Earlier work this paper cites.

G. Aarts, F. A. James, E. Seiler and I.-O. Stamatescu, Adaptive stepsize and instabilities in complex Langevin dynamics, Phys. Lett. B

2010

Earlier work this paper cites.

G. Aarts, E. Seiler and I.-O. Stamatescu, The Complex Langevin method: When can it be trusted?, Phys. Rev. D

2010

Earlier work this paper cites.

J. Nishimura, T. Okubo and F. Sugino, Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings, JHEP

2011

Cited alongside, same era.

G. Aarts, F. A. James, E. Seiler and I.-O. Stamatescu, Complex Langevin: Etiology and Diagnostics of its Main Problem, Eur. Phys. J. C

2011

Cited alongside, same era.

S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions, Phys. Rev. Lett

2012

Cited alongside, same era.

K. N. Anagnostopoulos, T. Azuma and J. Nishimura, Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models, JHEP

2013

Cited alongside, same era.

Y. Ito, S.-W. Kim, Y. Koizuka, J. Nishimura and A. Tsuchiya, A renormalization group method for studying the early universe in the Lorentzian IIB matrix model, PTEP

K. Nagata, J. Nishimura and S. Shimasaki, Argument for justification of the complex Langevin method and the condition for correct convergence, Phys. Rev. D

2016

Later among the works it cites.

Y. Ito and J. Nishimura, The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant, JHEP

2016

Later among the works it cites.

K. N. Anagnostopoulos, T. Azuma, Y. Ito, J. Nishimura and S. K. Papadoudis, Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models, JHEP

2018

Later among the works it cites.

T. Aoki, M. Hirasawa, Y. Ito, J. Nishimura and A. Tsuchiya, On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model, PTEP

2019

Later among the works it cites.

J. Nishimura and A. Tsuchiya, Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model, JHEP