Emergent Geometry and Gravity from Yang-Mills Matrix Models

Full text: Matrix Models of Yang-Mills type provide a remarkable pre-geometric approach to geometry and gravity. Space-time is described as a non-commutative brane solution of the model, i.e. as sub-manifold of RD. Gauge fields, scalar fields and matter arise on the brane as fluctuations of the matrices around such a background, and couple to an effective metric interpreted in terms of gravity. We show how curvature and physically relevant geometries can be realized in this framework. Several types of geometries are identified, in particular 'harmonic' and 'Einstein' type of solutions. The relation to non-commutative gauge theory and the role of UV/IR mixing is explained. The IKKT model with D=10 and close relatives are singled out as promising candidates for a quantum theory of fundamental interactions including gravity. (author)