Holomorphic analogs of topological gauge theories

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, Kähler and Calabi-Yau manifolds and describe their gauge symmetries. Candidate observables, topological invariants and relations to integrable models are briefly discussed.