Emergent Gravity from Noncommutative Spacetime

Nov, 2006
50 pages
Published in:
  • Int.J.Mod.Phys.A 24 (2009) 4473-4517
e-Print:
Report number:
  • HU-EP-06-21

Citations per year

20062011201620212024024681012
Abstract:
We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime. Gravity is then a collective phenomenon emerging from photons living in fuzzy spacetime. We elucidate in some detail why electromagnetism in NC spacetime should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form Bμν=(1/θ)μνB_{\mu\nu}=(1/\theta)_{\mu\nu}, giving rise to NC spacetime. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. As a corollary, we find evidences that the emergent gravity contains the structure of generalized complex geometry and NC gravity. To illuminate the emergent gravity from NC spacetime, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual spacetime. We also discuss derivative corrections of Seiberg-Witten map which give rise to higher order gravity.
  • 02.40.Gh
  • 04.50.+h
  • 11.10.Nx
  • Emergent gravity
  • noncommutative field theory
  • Seiberg-Witten map
  • gravitation: collective phenomena
  • space-time: noncommutative
  • differential geometry: symplectic
  • Seiberg-Witten map