In part 1 of this series of posts, I started a Kähler-Poincaré holomorphic BF action cohomology-analysis of the -symmetry, which fully determines a ring of topological 'observables', and thus derived from the symmetries of the action

given

in this post, part 2, I will analyze, among other relations, the following BRST-topological quantum field theory action

and set the stage for Calabi-Yau 3-folding analysis by showing that on a hyper-Kähler manifold, we can identify, via holonomy-group-Kähler-algebraic twisting, the gauge-fixed action with N = 1, D = 4 Yang–Mills action. Let me choose a BV gauge function

in order to gauge–fix the fermionic action - see below - to derive the N = 1, D = 4 chiral multiplet action

To characterize a quantum theory: a path integral, I need to gauge-fix the topological symmetry of the BF system in a way consistent with faithfulness to the BRST symmetry associated to this symmetry

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