One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model

Abstract

A detailed derivation of $3+1$ dimensional induced or emergent gravity in the IKKT matrix model at one loop is given, as announced in [1]. The mechanism requires a brane configuration with structure ${\mathcal{M}}^{3,1}\times \mathcal{K}\subset {\mathbb{R}}^{9,1}$, where ${\mathcal{M}}^{3,1}$ is the noncommutative space-time brane, and $\mathcal{K}$ are compact fuzzy extra dimensions embedded in target space. The 3+1-dimensional Einstein-Hilbert action then arises in the one loop effective action of the maximally supersymmetric IIB or IKKT matrix model, with effective Newton constant determined by the Kaluza-Klein scale of $\mathcal{K}$. At weak coupling, all physical modes are confined to the brane, leading to $3+1$-dimensional low-energy physics. The Einstein-Hilbert action can be interpreted as interaction of $\mathcal{K}$ with the space-time brane via IIB supergravity. The vacuum energy does not act as cosmological constant, but stabilizes the brane structure at one loop.

39 pages, 1 figure

References in corpus (4)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in $\mathcal{N}=4$ SYM and matrix models
• Heat kernel expansion and induced action for the matrix model Dirac operator