Non-linear realizations and invariant action principles in higher gauge theory

Abstract

We propose an extension of the formalism of non-linear realizations to the case of FDAs. We first consider the case of FDAs carrying one p-form extension and no non-trivial cohomology. We show that it is possible to define large gauge transformations as a direct extension of those induced by their Lie subalgebras, and study the resulting non-linear realizations. Furthermore, we extend the results to the case FDAs with non-trivial cohomology by introducing large gauge transformations that carry the information about the FDA cocycle structure constants. We consider two bosonic examples of this type of gauge algebra, namely, FDA extensions of the Poincaré and Maxwell algebras, write down their dual $L_{\infty }$ algebras and study their non-linear realizations and possible invariant action principles. Finally, consider a similar treatment on the FDA of $D=11$ supergravity, by deriving its dual algebra and presenting a non-linear realization that allows a gauge invariant formulation of its action principle.