# Instances of Higher Geometry in Field Theory

**Authors:** Athanasios Chatzistavrakidis  
**arXiv:** [2211.08097](https://arxiv.org/abs/2211.08097)  
**Date:** 2022-11-15  
**Summary page:** https://www.summarizepaper.com/en/paper/2211.08097v1/

## Key points

- Generalisations of geometry in field theory and quantization have led to a deeper understanding of physical phenomena.
- Athanasios Chatzistavrakidis explores the role of higher geometry in three specific applications within physics:
- Elucidating algebroid structures on bundles and Q-manifolds
- Relevance to key areas such as Batalin-Vilkovisky quantization, higher gauge theories, generalized global symmetries, and tensor gauge theories
- Highlighting the universality of geometric forms and properties in graded geometry for advancing understanding of complex physical systems.
- Higher geometry is a powerful tool for unraveling intricate relationships within field theory and quantization, paving the way for future advancements in theoretical physics.

## Summary

In the study of field theory and quantization, generalisations of geometry have taken on various forms. These have led to a deeper understanding of physical phenomena. In this mini-review, Athanasios Chatzistavrakidis delves into the role of higher geometry in three specific applications within the realm of physics. The exploration begins by elucidating the fundamental aspects of algebroid structures on bundles and (differential graded) Q-manifolds. This sets the stage for a discussion on their relevance to key areas such as ($\alpha$) the Batalin-Vilkovisky quantization of topological sigma models, ($\beta$) higher gauge theories and generalized global symmetries, and ($\gamma$) tensor gauge theories. By highlighting the universality of these geometric forms and properties in terms of graded geometry, Chatzistavrakidis sheds light on how these concepts play a crucial role in advancing our understanding of complex physical systems. Through this exploration, it becomes evident that higher geometry serves as a powerful tool for unraveling intricate relationships within field theory and quantization. This review not only provides valuable insights into current research but also paves the way for future advancements in theoretical physics.