Homotopy momentum sections on multisymplectic manifolds
arXiv:2110.12305 · doi:10.1016/j.geomphys.2022.104667
Abstract
We introduce a notion of a homotopy momentum section on a Lie algebroid over a pre-multisymplectic manifold. A homotopy momentum section is a generalization of the momentum map with a Lie group action and the momentum section on a pre-symplectic manifold, and is also regarded as a generalization of the homotopy momentum map on a multisymplectic manifold. We show that a gauged nonlinear sigma model with Wess-Zumino term with Lie algebroid gauging has the homotopy momentum section structure.
arXiv comment32pages
References in corpus (18)
- WZW-Poisson manifolds
- Lectures on Integrability of Lie Brackets
- Multi-moment maps
- Closed forms and multi-moment maps
- Groupoid symmetry and constraints in general relativity
- Lie Algebroid Yang Mills with Matter Fields
- Lie algebroids, gauge theories, and compatible geometrical structures
- Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
- Reduction of multisymplectic manifolds
- T-duality without isometry via extended gauge symmetries of 2D sigma models
- Strings in Singular Space-Times and their Universal Gauge Theory
- Noether's Theorem in Multisymplectic Geometry
- Existence and unicity of co-moments in multisymplectic geometry
- Conserved quantities on multisymplectic manifolds
- Momentum sections in Hamiltonian mechanics and sigma models
- Momentum section on Courant algebroid and constrained Hamiltonian mechanics
- Gauging as constraining: the universal generalised geometry action in two dimensions
- Lie Algebroid Gauging of Non-linear Sigma Models