Emergent gravity on covariant quantum spaces in the IKKT model

Abstract

We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields. They arise from an internal structure which can be viewed as a twisted bundle over $S^4$, leading to a covariant noncommutative geometry. The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions, modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.

38+8 pages, 1 figure. V2: substantial revision: extension to thick spheres and rank 3 tensor, modified conclusion. V3: more transparent analysis of gravity modes, typos fixed