Aganagic, MinaKlemm, AlbrechtMario, MarcosVafa, Cumrun2019-09-222004Aganagic, Mina, Albrecht Klemm, Marcos Mari�o, and Cumrun Vafa. 2004. “The Topological Vertex.” Communications in Mathematical Physics 254 (2): 425–78. https://doi.org/10.1007/s00220-004-1162-z.0010-36161432-0916http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385008We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.en-USJournal Article2019-09-2210.1007/s00220-004-1162-z