Noncommutative Spacetime and Emergent Gravity
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 \theta for the picture (II).
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.0234
 Bibcode:
 2007arXiv0711.0234Y
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 Mathematics  Symplectic Geometry
 EPrint:
 4 pages