Holomorphic field theories and Calabi-Yau algebras - Eager, Richard; Saberi, Ingmar (Arxiv, 2018)
We consider the holomorphic twist of the worldvolume theory of flat D(2k-1)-branes transversely probing a Calabi-Yau manifold. A chain complex, constructed using the BV formalism, computes the local observables in the holomorphically twisted theory. Generalizing earlier work in the case k=2, we find that this complex can be identified with the Ginzburg dg algebra associated to the Calabi-Yau. However, the identification is subtle; the complex is the space of fields contributing to the holomorphic twist of the free theory, and its differential arises from interactions. For k=1, this holomorphically twisted theory is related to the elliptic genus. We give a general description for D1-branes probing a Calabi-Yau fourfold singularity, and for N=(0,2) quiver gauge theories.