Homotopy momentum sections on multisymplectic manifolds

TL;DR

This paper introduces homotopy momentum sections on multisymplectic manifolds, generalizing momentum maps and homotopy momentum maps, and demonstrates their application in gauged nonlinear sigma models with Wess-Zumino terms.

Contribution

It defines homotopy momentum sections on Lie algebroids over pre-multisymplectic manifolds, extending existing concepts and linking them to physical models.

Findings

Homotopy momentum sections generalize classical momentum maps.

Application to gauged nonlinear sigma models with Wess-Zumino terms.

Establishes a new geometric structure in multisymplectic geometry.

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.