1202.6306 (Harold Steinacker)

Gravity and compactified branes in matrix models    [PDF]

Harold Steinacker

The mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is clarified. Newtonian gravity and Ricci-flat 4-dimensional vacuum geometry can arise from the basic matrix model action, without invoking an Einstein-Hilbert-type term. The key requirements are compactified extra dimensions with extrinsic curvature M^4 x K \subset R^D and split noncommutativity, with a Poisson tensor linking the compact with the noncompact directions. The degrees of freedom for gravity are encoded in the moduli of the compactification, which are transmitted to the noncompact directions via the Poisson tensor. The Einstein tensor is coupled to the energy-momentum tensor in a modified way, and deviations from general relativity depend on the compactification. The effective Newton constant is determined by the scale of noncommutativity and the compactification. This gravity theory is well suited for quantization, and argued to be perturbatively finite for the IKKT model. Since no compactification of the target space is needed, it may provide a way to avoid the landscape problem in string theory.

View original: http://arxiv.org/abs/1202.6306