Holomorphic field theories and Calabi--Yau algebras

Understand

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.