THE TOPOLOGICAL B-MODEL AS A TWISTED SPINNING PARTICLE

The B-twisted topological sigma model coupled to topological gravity i s supposed to be described by an ordinary field theory: a type of holo morphic Chem-Simons theory for the open string, and the Kodaira-Spence r theory for the closed string. We show that the B model can be repres ented as a particle theory, obtained by reducing the sigma model to on e dimension, and replacing the coupling to topological gravity by a co upling to a twisted one-dimensional supergravity. The particle can be defined on any Kahler manifold-it does not require the Calabi-Yau cond ition-so it may provide a more generalized setting for the B model tha n the topological sigma model. The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the mani fold, and agrees with that of the original B model. After showing how to deform the Kahler and complex structures in the particle, we prove the independence of this partition function on the Kahler structure, a nd investigate the origin of the holomorphic anomaly. To define other amplitudes, one needs to introduce interactions into the particle. The particle will then define a field theory, which may or may not be the Chern-Simons or Kodaira-Spencer theories.