Symmetry, gravity and noncommutativity

2006/06/30 by Richard J. Szabo, Richard J Szabo · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #General relativity #Homogeneous space #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum differential calculus #Spacetime #String theory #Superstring theory #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/23/22/r01

published as Class.Quant.Grav.23:R199-R242,2006 · 52 pages; Invited review article to be published in Classical and Quantum Gravity; v2: references added

arxiv created 2006/07/04 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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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Cited by

• Towards A Background Independent Quantum Gravity