Noncommutative Spacetime and Emergent Gravity
arXiv:0711.0234
Abstract
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix model or a large N field theory where NC fields can be regarded as master fields of large N matrices. (II) NC fields essentially define vector (tetrad) fields. So they define a gravitational metric of some manifold as an emergent geometry from NC gauge fields. Of course, the pictures (I) and (II) should refer to the same physics, which should be familiar with the large N duality in string theory. The 1/N corrections in the picture (I) correspond to the derivative corrections in terms of the noncommutativity θfor the picture (II).
4 pages; To appear in Proceedings (Lie Theory and Its Applications in Physics VII, ed. V.K. Dobrev et al, Heron Press, Sofia, 2008) of the 7th International Workshop "Lie Theory and Its Applications in Physics", 18-24 June 2007, Varna, Bulgaria