Symmetry, Gravity and Noncommutativity

TL;DR

This paper reviews how noncommutative geometry influences spacetime symmetries and explores their role in formulating theories of gravity derived from string theory, highlighting the connection between noncommutative gauge theories and gravity.

Contribution

It provides a detailed analysis of noncommutative gauge transformations, their relation to gravity, and the construction of noncommutative extensions of general relativity based on twisted symmetries.

Findings

Noncommutative Yang-Mills theory can be related to gravity.

Twisted spacetime symmetries enable noncommutative gravity models.

Examples of noncommutative gauge theories on D-branes in curved backgrounds.

Abstract

We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it is shown how noncommutative Yang-Mills theory can be related to a gravity theory. The construction of twisted spacetime symmetries and their role in constructing a noncommutative extension of general relativity is described. We also analyse certain generic features of noncommutative gauge theories on D-branes in curved spaces, treating several explicit examples of superstring backgrounds.