Emergent Gravity from Noncommutative Spacetime
Nov, 200650 pages
Published in:
- Int.J.Mod.Phys.A 24 (2009) 4473-4517
e-Print:
- hep-th/0611174 [hep-th]
Report number:
- HU-EP-06-21
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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 , 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
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