Instances of Higher Geometry in Field Theory

TL;DR

This paper reviews how advanced geometric structures like algebroids and Q-manifolds underpin modern field theory topics such as topological models, higher gauge theories, and tensor gauge theories, emphasizing their universal graded geometric framework.

Contribution

It highlights the role of higher geometric structures in unifying various aspects of field theory and quantization, providing a concise overview of their applications.

Findings

Higher geometry structures underpin topological sigma models

They unify higher gauge theories and generalized symmetries

Graded geometry offers a universal framework for these theories

Abstract

Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some basic aspects of algebroid structures on bundles and (differential graded) Q-manifolds, we briefly discuss their relation to ($\alpha$) the Batalin-Vilkovisky quantization of topological sigma models, ($\beta$) higher gauge theories and generalized global symmetries and ($\gamma$) tensor gauge theories, where the universality of their form and properties in terms of graded geometry is highlighted.