The Gromov-Witten potential associated to a TCFT

摘要: This is the sequel to my preprint "TCFTs and Calabi-Yau categories", math.QA/0412149. Here we extend results of that paper construct, for certain A-infinity categories, something playing role Gromov-Witten potential. a state in Fock space associated periodic cyclic homology, which symplectic vector space. Applying this suitable version derived category sheaves on yields B model potential, at all genera. The construction doesn't go via Deligne-Mumford spaces, but instead uses Batalin-Vilkovisky algebra constructed from uncompactified moduli spaces curves by Sen Zwiebach. The fundamental class replaced here solution quantum master equation, essentially "string vertices" On field theory side, BV operator has an interpretation as quantised differential chains. Passing satisfying equation element