A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

Abstract

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Using this method, one can obtain the results for N × N matrices by simulating matrices typically of the size O( √ N ). We confirm the validity of this method and demonstrate its usefulness in simplified models.

On the structure of the emergent 3D expanding space in the Lorentzian type IIB matrix model

“…This connection also provides clear justification of the renormalization-group-like method[9,35], which amounts to tuning the parameter C in order to obtain the late-time behaviors with smaller matrix size.…”

“…This can be obtained by integrating out the overall scale factor of the bosonic matrices A µ first and using certain approximation as discussed in section 4. The parameter C should be set to zero according to the "derivation", but we generalize the model by choosing C = 0, which allows us to obtain results for larger matrices in the original C = 0 model by using smaller matrices [9,35]. See Appendix B of ref.…”

New perspectives on the emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model

“…In ref. [1] as well as in more recent work [20][21][22][23] on the Lorentzian type IIB matrix model and its simplified models, the sign problem was avoided by integrating out the scale factor of the bosonic matrices by hand, which yields a function of the bosonic action S b sharply peaked at the origin. Approximating this function by a sharply peaked Gaussian function, we can perform Monte Carlo simulations without the sign problem.…”

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

“…In ref. [2] and our subsequent work [15][16][17][18] on the Lorentzian type IIB matrix model and its simplified models, the sign problem was avoided by integrating out the scale factor of the bosonic matrices by hand, which yields a function of the bosonic action S b sharply peaked at the origin. Approximating this function by a sharply peaked Gaussian function, we can perform Monte Carlo simulations without the sign problem.…”

“…18) and the PfM (A) in (2.10) should be replaced by PfM(e −ikπ/2 A 0 , A i ). The Lorentzian model is retrieved at (s, k) = (0, 0), whereas the Euclidean model corresponds to setting (s, k) = (1, 1).…”