Heriot-Watt Mathematics Report Series
HWM06-29, 23 Jun 2006
Symmetry, gravity and noncommutativity
R J Szabo
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.
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