Holomorphic Analogs of Topological Gauge Theories

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.

12 pages, LaTeX2e, shortened PLB version

References in corpus (2)

• Self-Dual Yang-Mills: Symmetries and Moduli Space
• Holomorphic Chern-Simons-Witten Theory: from 2D to 4D Conformal Field Theories

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• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
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• One-dimensional structures behind twisted and untwisted superYang-Mills theory
• Twisted N=1, d=4 supergravity and its symmetries
• Integrable models from 4d holomorphic BF theory