An elucidation on the geometrization of electromagnetic force further leads to a proposal for a gravity theory (which we call emergent gravity) with non-symmetric metric. It will be shown why we believe that in noncommutative (NC) spacetime there always exists a coordinate transformation that locally eliminates electromagnetic force which is nothing but an upshot of Darboux theorem (precisely an analogue of equivalence principle) in symplectic geometry. The consequence is that electromagnetism can be realized as a geometrical property of spacetime like gravity. It will be discussed how emergent gravity reveals a beautiful generalized geometrical structure which is an artifact of the famous Seiberg-Witten equivalence between commutative and NC DBI actions and is reminiscent of the homological mirror symmetry. Further physical motivations will be explicated if time permits.
Venue: Department of Mathematics, Trieste University, Seminar Room - Third Floor bld H2bis