Generalized sigma model with dynamical antisymplectic potential and non-Abelian de Rham's differential

TL;DR

This paper introduces a generalized sigma model framework where the Lagrangian depends non-linearly on de Rham velocities, leading to a dynamical antisymplectic structure that satisfies the master equation.

Contribution

It proposes a novel approach to topological sigma models by defining a dynamical antisymplectic potential and metric based on the Lagrangian's dependence on de Rham velocities.

Findings

Defined a dynamical antisymplectic potential and metric.

Established the local and functional antibrackets using the dynamical metric.

Proved the generalized action satisfies the functional master equation.

Abstract

For topological sigma models, we propose that their local Lagragian density is allowed to depend non-linearly on the de Rham's "velocities" $D Z^{A}$. Then, by differentiating the Lagrangian density with respect to the latter de Rham's "velocities", we define a "dynamical" anti-symplectic potential, in terms of which a "dynamical" anti-symplectic metric is defined, as well. We define the local and the functional antibracket via the dynamical anti-symplectic metric. Finally, we show that the generalized action of the sigma model satisfies the functional master equation, as required.