A higher stacky perspective on Chern-Simons theory

TL;DR

This paper explores an advanced geometric framework for Chern-Simons theory, extending traditional concepts to higher structures, unifying action functionals, prequantum bundles, and WZW models within a comprehensive higher prequantum field theory.

Contribution

It introduces a higher geometric perspective on Chern-Simons theory, unifying various aspects of quantum field theory through extended prequantum structures and higher geometric descriptions.

Findings

Localization of the Chern-Simons action to a universal moduli stack

Unification of action, prequantum bundle, and WZW functional via transgression

Extension to higher prequantum field theory including supersymmetry and anomalies

Abstract

The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern-Simons theory is naturally localized ("extended", "multi-tiered") to a map on the universal moduli stack of principal connections, a map that itself modulates a circle-principal 3-connection on that moduli stack, and how the iterated transgressions of this extended Lagrangian unify the action functional with its prequantum bundle and with the WZW-functional. In the second part we provide a brief review and outlook of the higher prequantum field theory of which this is a first example. This includes a higher geometric description of supersymmetric Chern- Simons theory, Wilson loops and other defects, generalized geometry, higher Spin structures, anomaly cancellation, and various other aspects of quantum field theory.