Gravity as a Quantum Effect on Quantum Space-Time

TL;DR

This paper derives the Einstein-Hilbert action from a matrix model framework, showing gravity as an emergent quantum effect influenced by noncommutative geometry and supersymmetry.

Contribution

It demonstrates how gravity arises from noncommutative branes in matrix models, linking the Einstein-Hilbert action to underlying quantum and geometric structures.

Findings

Einstein-Hilbert action derived from matrix models with noncommutative branes.

Effective Newton constant linked to Kaluza-Klein scale of extra dimensions.

Vacuum energy does not contribute to cosmological constant.

Abstract

The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions ${\cal K}$ as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of ${\cal K}$ with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of ${\cal K}$. The bare matrix model defines a pre-gravity action with 2 derivatives less than the induced E-H action, governing the cosmological regime. The perturbative physics is confined to the space-time brane, which for covariant quantum space-times includes all dof of gravity, as well as a tower of higher-spin modes. The vacuum energy is given in terms of the symplectic volume form, and hence does not act as cosmological constant.