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

Abstract

The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding spacetime was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.

Limitations of an effective field theory treatment of early Universe cosmology

“…In the limit N → ∞, this gives us continuous time t, where t is obtained by averaging the diagonal elements of A 0 over a range n of values (where n N but n being a fixed fraction of N as N → ∞). The key observation of the work summarized in [98] is that in the large N limit, the matrices A i , i = 1, . .…”

“…In the limit Nfalse→normal∞, this gives us continuous time t, where t is obtained by averaging the diagonal elements of A0 over a range n of values (where n≪N but n being a fixed fraction of N as Nfalse→normal∞). The key observation of the work summarized in [98] is that in the large N limit, the matrices Ai,i=1,…,9 become block diagonal, with elements outside of n×n blocks being greatly suppressed. For time t, we have spatial blocks Afalse¯ifalse(tfalse) which in the limit Nfalse→normal∞ become continuous space.…”

Emergent metric space-time from matrix theory

“…The IKKT matrix model [14] (see [15][16][17] for recent reviews) has been proposed as a non-perturbative definition of Type IIB superstring theory. It is a pure matrix theory (no space and no time), given by the action…”

“…Over the past two decades there has been a lot of numerical work on this model (see e.g. [15][16][17] for reviews, and [18][19][20] for more recent numerical studies), and we will summarize the results which are relevant for our analysis. In section 3, we then show how continuous space-time with infinite extent of both space and time variables emerges, give a proposal for an emergent metric, and show that the resulting cosmological metric corresponds to a spatially flat manifold.…”

Fundamental Physics, the Swampland of Effective Field Theory and Early Universe Cosmology

“…In the limit N → ∞ this gives us continuous time t, where t is obtained by averaging the diagonal elements ofA 0 over a range n of values (where n N but n being a fixed fraction of N as N → ∞). The key observation of the work summarized in [60] is that in the large N limit, the matrices A i , i = 1, ...., 9 become block diagonal, with elements outside of n × n blocks being greatly suppressed. For time t, we have spatial blocksĀ i (t) which in the limit N → ∞ become continuous space.…”