Quantum gravity equation in largeNYang-Mills quantum mechanics

Abstract

We propose a new interpretation of the BFSS large N matrix quantum mechanics analogous to a novel interpretation of the IKKT matrix model where infinitely large N matrices act as differential operators in a curved space. In this picture, the Schrödinger equation in the BFSS model is regarded as the Wheeler-DeWitt equation which determines the wave function of universe. An explicit solution of wave function is studied in a simple two-dimensional minisuperspace model.

A renormalization group method for studying the early universe in the Lorentzian IIB matrix model

“…Integrating out A i at the one-loop level, one obtains ∆(α) −18 neglecting the zero modes corresponding to diagonal elements. Integrating out Ψ α at the one-loop level, one obtains ∆(α) 16 neglecting the zero modes. Thus one finds that the ∆(α) 2 in (2.17) is canceled exactly at the one-loop level, which is actually a consequence of the supersymmetry [5] of the model (2.4).…”

“…These models can be obtained formally 1 by dimensionally reducing ten-dimensional N = 1 super Yang-Mills theory to d = 0, 1, 2 dimensions, respectively. Based on these proposals, various issues of the early universe have been discussed [8][9][10][11][12][13][14][15][16][17]. As a closely related direction, ref.…”

Late time behaviors of the expanding universe in the IIB matrix model

“…For earlier attempts to apply matrix models to cosmology, see ref [9][10][11][12][13][14][15][16][17][18][19]…”

Classical solutions of a torsion gravity from a largeNmatrix model

“…It is contrast to PGT, in which an asymptotically flat solution has been found analytically [15] (several asymptotically nonflat solutions were also found [16]). This would imply that torsions in our study are constrained to be very small in physically acceptable solutions, in order to well describe the solar system in present day 9 . However this observation itself does not prohibit a possibility of finding some solutions with a large effect of torsion in past or future period, which describes possible evolutions of the universe .…”

“…They applied this new interpretation (we call this interpretation "HKK interpretation" or simply "HKK" for later convenience) to the IKKT matrix model [1], and derived the Einstein equation in empty space from the classical matrix equation of motion. Several studies have been done to explore this attractive proposal [5,6,7,8,9] 3 .…”