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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!

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What do people mean when they refer to a 'master equation'? – Minhyong Kim May 26 2010 at 23:02
That's the master equation associated to a (dg)BV algebra. – HYYY May 27 2010 at 2:43

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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..

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Thanks!(I once assumed that's the paper by Kontsevich and Bananikov) Can we get the same thing for A model?(using his method). That's what exactly Costello once guided me, there is no such construction for A model currently. That's what I am confused here. But I do construct similar things for A model recently. – HYYY May 27 2010 at 2:42

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