Reduction over coset spaces and residual gauge symmetry. (English) Zbl 1392.81209

Summary: 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 \(S^7\) to the Lie group submanifold \(S^3\times S^3\) is considered. The structure of an octonionic Chern-Simons gauge theory is described.


81T60 Supersymmetric field theories in quantum mechanics
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
Full Text: Euclid