Reduction over Coset Spaces and Residual Gauge SymmetryDavis S*
Research Foundation of Southern California, 8837 Villa La Jolla Drive #13595 La Jolla, California, USA
- *Corresponding Author:
- Davis S
Research Foundation of Southern California
8837 Villa La Jolla Drive #13595 La Jolla
E-mail: [email protected]
Received Date: May 30, 2016; Accepted Date: July 09, 2016; Published Date: December 30, 2016
Citation: Davis S (2016) Reduction over Coset Spaces and Residual Gauge Symmetry. J Generalized Lie Theory Appl 10:249. doi:10.4172/1736-4337.1000249
Copyright: © 2016 Davis S. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The reduction of higher-dimensional theories over a coset space S/R is known to yield a residual gauge symmetry related to the number of R-singlets in the decomposition of S with respect to R. It is verified that this invariance is identical to that found by requiring that there is a subgroup of the isometry group with an action on the connection form that yields a transformation rule defined only on the base space. The Lagrangian formulation of the projection of the frame of global vector fields from S7 to the Lie group submanifold S3× S3 is considered. The structure of an octonionic Chern-Simons gauge theory is described.