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Algebroid Yang-Mills theories
1TPI, FSU-Jena, Max-Wien-Platz 1, D-07743 Jena, Germany. pth@tpi.uni-jena.de
Physical Review Letters
|December 17, 2004
Summary
This study introduces a new framework for gauge theories by replacing Lie algebras with algebroids. This approach yields novel topological theories and deforms Yang-Mills theories with additional fields acting as moduli, enhancing symmetry.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Mathematical Physics
Background:
- Gauge theories are fundamental in describing particle interactions.
- Lie algebras are the mathematical foundation for standard gauge theories.
- Existing frameworks may limit the exploration of novel physical phenomena.
Purpose of the Study:
- To propose a generalized framework for constructing gauge theories.
- To explore topological theories in arbitrary dimensions.
- To investigate deformations of Yang-Mills theories using algebroids.
Main Methods:
- Replacing Lie algebras with Lie or Courant algebroids.
- Introducing fiber metrics with E-Killing vectors on Lie algebroids.
- Analyzing the properties of resulting field theories.
Main Results:
- Construction of novel topological gauge theories in arbitrary spacetime dimensions.
- Development of a mild deformation of Yang-Mills theories.
- Identification of additional fields that act as moduli parameters, not propagating modes.
- Observation of symmetry enhancement at critical points of these moduli fields.
Conclusions:
- The proposed algebroid framework offers a novel approach to gauge theory construction.
- This generalization leads to new topological theories and modified Yang-Mills theories.
- The findings suggest a connection to string effective field theories through symmetry enhancement.