Higher dimensional Lie algebroid sigma model with WZ term

TL;DR

This paper extends a class of topological sigma models to higher dimensions using Lie algebroids, identifying geometric conditions for their consistency related to multi-symplectic structures.

Contribution

It introduces a generalized framework for higher-dimensional sigma models with Lie algebroid structures and establishes universal compatibility conditions for their geometric consistency.

Findings

Identifies geometric conditions for consistent higher-dimensional sigma models.

Generalizes momentum map and momentum section concepts to Lie algebroids.

Provides a Hamiltonian and Lagrangian formalism analysis for the models.

Abstract

We generalize the $(n+1)$-dimensional twisted $R$-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the Lagrangian formalism, geometric conditions of the target space to make the topological sigma model consistent are identified. The geometric condition is an universal compatibility condition of a Lie algebroid with the multi-symplectic structure. This condition is a generalization of the momentum map theory of a Lie group and is regarded as a generalization of the momentum section condition of the Lie algebroid.