Holomorphic field theories and Calabi–Yau algebras

We consider the holomorphic twist of the worldvolume theory of flat D[Formula: see text]-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 [Formula: see text], 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 [Formula: see text], 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 [Formula: see text] quiver gauge theories. In addition, we propose a relation between the equivariant Hirzebruch [Formula: see text] genus of large-[Formula: see text] symmetric products and cyclic homology.

Research of a Supersonic Axial Vaneless Rotor-Rotor Turbine

A supersonic vaneless rotor-rotor turbine (abbr.RRT) which only consists of upstream rotor and downstream rotor rotating in opposite direction is presented to investigate its aerodynamic characters and performance in the paper. The methods of both controlled vortexes and controlled meridional contours are adopted in the through-flow design and analysis of RRT. The counter twisted theory, which is usually used in the stationary vanes is employed the upstream rotor of RRT to adjust its exit angular momentum. The stagnation efficiency of RRT was 94.2% which is about higher 3% than the conventional turbine with the same shaft power. The results of 3D simulation of RRT indicated that it is very important to adopt the method of controlled vortexes to design the upstream rotor in order to improve its aerodynamic performance on condition that its vanes are eliminated completely.