Quantum spacetime and quantum fluctuations in the IKKT model at weak coupling

TL;DR

This paper explores the emergent structure of spacetime in IKKT matrix models, identifying key scales of noncommutativity and quantum fluctuations, and clarifying their roles in semi-classical and quantum regimes.

Contribution

It clarifies how meaningful coupling constants and uncertainty scales emerge in IKKT models without adjustable parameters, supporting semi-classical geometry and quantum gravity studies.

Findings

Quantum fluctuations are negligible at weak coupling.

Two regimes are distinguished: semi-classical noncommutative geometry and deep quantum holography.

The work supports previous models of emergent 3+1-dimensional spacetime.

Abstract

This paper aims to clarify conceptual aspects of emergent structure in IKKT-type matrix models. Even without any adjustable parameters in the action, non-trivial matrix vacua do acquire a meaningful coupling constant, as well as two distinct uncertainty scales: a) the scale of noncommutativity of the matrix background, and b) the scale of quantum fluctuations of the matrices under the path integral. These scales are estimated for two prototypes of matrix backgrounds, known as Moyal-Weyl quantum plane and covariant quantum spacetime. Their relative importance separates two regimes: 1) the semi-classical regime interpreted in terms of semi-classical noncommutative geometry, and 2) the deep quantum regime usually interpreted in terms of holography. The quantum fluctuations are shown to be negligible in the weak coupling regime. This justifies previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.