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 $$ {\mathcal{M}}^{3,1}\times \mathcal{K}\subset {\mathbb{R}}^{9,1} $$ M 3 , 1 × K ⊂ ℝ 9 , 1 , where $$ {\mathcal{M}}^{3,1} $$ M 3 , 1 is the noncommutative space-time brane, and $$ \mathcal{K} $$ 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 $$ \mathcal{K} $$ 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 $$ \mathcal{K} $$ 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.

IKKT thermodynamics and early universe cosmology

“…However, numerical evidence suggests that such a process is realizable in matrix theory [30]. The details of this transition are currently under study (see [31] for progress on this topic, also see for an [32,33] alternate approach to trying to solve this problem). It could be interesting to figure out the connection between these results for the traditional world sheet description of the superstring, and its matrix description.…”

The emergence of expanding space-time in the Lorentzian type IIB matrix model with a novel regularization

“…See Ref. [17][18][19][20][21] for other recent studies on the type IIB matrix model, in which possible applications to cosmology are discussed.…”