I was heard (by an expert) that, in mirror symmetry, we have constructed a Quantum Master Equation associated to topological B model, and a solution to it. But I can't find any material about this. Is there anyone know anything about this, so you can give me some help? Is that Kontsevich and Bananikov's paper (for genus 0 topological B model on Calabi-Yau)?? And is the sullivan's paper "Sigma model and string topology" related to this to some extent?(but I can't see what the useness is of this one).Thank you very much for your help!
This is the subject of this paper by Kevin Costello -- he constructs a solution to a master equation associated to a Calabi-Yau category, which one could take to be the category of branes in the topological B-model. (See the article for references to work of Sen and Zwiebach in the physics literature). String topology can be thought of as a kind of simplified B-model, so Sullivan's paper is also related I presume but haven't looked..