TOPICAL REVIEW: Emergent geometry and gravity from matrix models: an introduction
Abstract
An introductory review to emergent noncommutative gravity within YangMills matrix models is presented. Spacetime is described as a noncommutative brane solution of the matrix model, i.e. as a submanifold of {\mathbb R}^D. Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semiclassical limit. The relation to noncommutative gauge theory and the role of UV/IR mixing are explained. Several types of geometries are identified, in particular 'harmonic' and 'Einstein' types of solutions. The physics of the harmonic branch is discussed in some detail, emphasizing the nonstandard role of vacuum energy. This may provide a new approach to some of the big puzzles in this context. The IKKT model with D = 10 and close relatives are singled out as promising candidates for quantum theory of fundamental interactions including gravity.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 July 2010
 DOI:
 10.1088/02649381/27/13/133001
 arXiv:
 arXiv:1003.4134
 Bibcode:
 2010CQGra..27m3001S
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Invited topical review for Classical and Quantum Gravity. 57 pages, 5 figures. V2,V3: minor corrections and improvements. V4,V5: some improvements, refs added