Courant-like brackets and loop spaces

TL;DR

This paper explores the algebraic structures of local functionals with Poisson brackets, focusing on Courant-Dorfman algebra analogues and their realization in superloop space functionals.

Contribution

It introduces Courant-like brackets in the context of local functionals and superloop spaces, expanding the algebraic framework of Poisson structures.

Findings

Identification of Courant-Dorfman algebra structures in local functionals

Examples of Courant-like brackets from superloop space analysis

Connections between algebraic structures and geometric loop space models

Abstract

We study the algebra of local functionals equipped with a Poisson bracket. We discuss the underlying algebraic structures related to a version of the Courant-Dorfman algebra. As a main illustration, we consider the functionals over the cotangent bundle of the superloop space over a smooth manifold. We present a number of examples of the Courant-like brackets arising from this analysis.