Holomorphic Analogs of Topological Gauge Theories

TL;DR

This paper develops a new class of holomorphic gauge theories on complex manifolds, extending topological gauge theories like Chern-Simons and BF to complex dimensions with potential applications in invariants and integrable models.

Contribution

It introduces holomorphic analogs of topological gauge theories on complex manifolds, including actions, gauge symmetries, and potential observables, expanding the theoretical framework.

Findings

Defined holomorphic BF theories on various complex manifolds

Described gauge symmetries and candidate observables

Discussed relations to integrable models

Abstract

We introduce a new class of gauge field theories in any complex dimension, based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are holomorphic analogs of the well-known Chern-Simons and BF topological theories defined on real manifolds. We introduce actions for different special holomorphic BF theories on complex, Kahler and Calabi-Yau manifolds and describe their gauge symmetries. Candidate observables, topological invariants and relations to integrable models are briefly discussed.