On The Correspondence Between Noncommuative Field Theory And Gravity

TL;DR

This paper reviews the emerging correspondence between noncommutative field theories and gravity, highlighting how gauge theories in noncommutative spacetime can give rise to gravitational phenomena.

Contribution

It clarifies the theoretical basis for the NCFT/Gravity correspondence, emphasizing the role of $ ext{Lambda}$-symmetry and Darboux theorem in linking gauge theories to gravity.

Findings

Gauge theories in NC spacetime can be interpreted as theories of gravity.

Gravity emerges as a collective phenomenon from gauge fields in fuzzy spacetime.

The $ ext{Lambda}$-symmetry acts similarly to diffeomorphisms, underpinning the correspondence.

Abstract

In this brief review, I summarize the new development on the correspondence between noncommuative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. I 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 $\Lambda$-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.