In part 1 of this series of posts, I started a Kähler-Poincaré holomorphic BF action cohomology-analysis of the $\delta$-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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The highest form of pure thought is in mathematics ~ Plato

That the Poincaré supersymmetry is a phase of a deeper symmetry is evidenced by the fact that it is analytically related to a class of topological symmetries and that the field-spectrum of dimensionally reduced $N = 1$ $D = 11$ supergravity is completely determined in the context of an 8-dimensional gravitational topological quantum field theory (TQFT). Let me study the Kähler-holomorphic nature of such connections by first analyzing the holomorphic BF action

with holomorphic sectorial localization constraints

The aim of this series of posts is ultimately the Kähler-Poincaré analysis of the action