Adiabaticity and emergence of classical space-time in time-dependent matrix theories

Abstract

We discuss the low-curvature regime of time-dependent matrix theories proposed to describe non-perturbative quantum gravity in asymptotically plane-wave space-times. The emergence of near-classical space-time in this limit turns out to be closely linked to the adiabaticity of the matrix theory evolution. Supersymmetry restoration at low curvatures, which is crucial for the usual space-time interpretation of matrix theories, becomes an obvious feature of the adiabatic regime.

Aspects of plane wave (matrix) string dynamics

“…We investigated the way that the dilaton depends on the regularisation, and found that the strongest constraints from dilaton regularity actually come from the elimination of diverging linear dilatons at large times t. This would be relevant if one thinks of this as a model for big bang and emergent spacetime, in the spirit of [17]. However, in that case one needs to study the late-time behaviour of the non-Abelian theory [24,44,45]. On the other hand if, in the spirit of the Penrose limit, one considers the plane wave only as a near-singularity approximation of the full metric, then the large-t behaviour is irrelevant simply because it is also an artefact of the approximation.…”

Matrix model approach to cosmology

“…Space-time geometry, field theory and gravity have been shown to dynamically emerge from matrix models. [1], [2], [3], [4], [5], [6], [7] Moreover, black hole and cosmological space-times were recovered in certain limits of matrix model solutions. [8], [9], [10], [11], [12], [13], [14] Matrix models were introduced by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT) [15] and Banks, Fischler, Shenker, and Susskind (BFSS) [16] in order to represent nonperturbative aspects of string theory.…”

“…Much progress has been made by evaluating the quantum partition function for the IKKT model in Euclidean and Minkowski space. [1], [3], [4], [5], [6], [14] In [14] it was the demonstration that the rotational invariance of nine spatial dimensions in the IKKT matrix model is spontaneously broken to SO(3) acting with the defining representation on three spatial dimensions. This gives justification for studying a simpler version of the IKKT model written in less than ten dimensions, with the possible addition of terms in the action which preserve the symmetries of the lower dimensional space-time.…”

Light-like big bang singularities in string and matrix theories

“…The issue may be technically somewhat involved, since geometrical notions appear rather indirectly in the matrix formalism. Heuristic results appeared in [36,52]; a systematic analysis has recently been carried out in [53], the results of which we now review.…”