Instances of higher geometry in field theory

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.