Graded geometry in gauge theories and beyond
arXiv:1411.4486 · doi:10.1016/j.geomphys.2014.07.001
Abstract
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using this concept we describe a procedure for analysis of gauge symmetries of given functionals as well as for constructing functionals (sigma models) invariant under an action of some gauge group. As the main example of application of these constructions we consider the twisted Poisson sigma model. We obtain it by a gauging-type procedure of the action of an essentially infinite dimensional group and describe its symmetries in terms of classical differential geometry. We comment on other possible applications of the described concept including the analysis of supersymmetric gauge theories and higher structures.
version accepted to Journal of Geometry and Physics, updated references
References in corpus (6)
- Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
- Generalizing Geometry - Algebroids and Sigma Models
- Formulation of gauge theories on transitive Lie algebroids
- Dirac Sigma Models from Gauging
- 2d Gauge Theories and Generalized Geometry
- Courant algebroids: Cohomology and Matched Pairs