Gravity as a Quantum Effect on Quantum Space-Time

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 $\mathcal{K}$ as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of $\mathcal{K}$ with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of $\mathcal{K}$. 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.

6 pages. V2: dilaton contribution corrected, references added, published version. V3: action corrected, conclusion unchanged

References in corpus (1)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model

Cited by in corpus (14)

• On the propagation across the big bounce in an open quantum FLRW cosmology
• Progress in the numerical studies of the type IIB matrix model
• Emergent Metric Space-Time from Matrix Theory
• A Twistorial Description of the IKKT-Matrix Model
• Fermions on curved backgrounds of matrix models
• One-loop effective action of the IKKT model for cosmological backgrounds
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Complex Langevin studies of the emergent space-time in the type IIB matrix model
• Emergent gravity from the IIB matrix model and cancellation of a cosmological constant
• String modes, propagators and loops on fuzzy spaces
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Spherically symmetric solutions of higher-spin gravity in the IKKT matrix model
• Intrinsic quantum dynamics of particles in brane gravity