The B model as a twisted spinning particle

TL;DR

This paper reformulates the B-twisted topological sigma model as a one-dimensional particle theory on any Kähler manifold, linking it to holomorphic Chern-Simons and Kodaira-Spencer theories, and explores its partition function and anomalies.

Contribution

It introduces a novel particle representation of the B model that does not require Calabi-Yau conditions, broadening the model's applicability and connecting it to one-dimensional supergravity.

Findings

Partition function expressed via Ray-Singer torsion.

Partition function independent of Kähler structure.

Framework for defining interactions and related field theories.

Abstract

The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string, and the Kodaira-Spencer theory for the closed string. We show that the B model can be represented as a PARTICLE theory, obtained by reducing the sigma model to one dimension, and replacing the coupling to topological gravity by a coupling to a twisted one-dimensional supergravity. The particle can be defined on ANY Kahler manifold--it does not require the Calabi-Yau condition--so it may provide a more generalized setting for the B model than the topological sigma model. The one-loop partition function of the particle can be written in terms of the Ray-Singer torsion of the manifold, 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, and 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.