ON THE CORRESPONDENCE BETWEEN NONCOMMUTATIVE FIELD THEORY AND GRAVITY

Abstract

In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.