B-strings on non-K\"ahlerian manifolds

TL;DR

This paper develops a framework for defining topological B-model strings on non-Kähler manifolds, emphasizing the role of superghost coupling and BV formalism for consistency and anomaly interpretation.

Contribution

It introduces a method to couple topological B-models on non-Kähler manifolds to topological gravity using BV formalism, addressing superghost effects and holomorphic anomaly.

Findings

Coupling of B-models to topological gravity on non-Kähler manifolds established

Superghost coupling is essential for consistent string model definition

Holomorphic anomaly interpretation clarified through superghost analysis

Abstract

We explain how to couple topological B-models whose targets are non-K\"ahlerian manifolds to topological gravity and to thus define corresponding topological strings. We emphasize the need to take into account the coupling to the superghost field of topological gravity in order to obtain a consistent definition of the string model. We also review the importance of the superghost for correctly interpreting the holomorphic anomaly of the string amplitudes. We perform our analysis in the BV framework in order to make it completely gauge independent.