2003/05/31 by Mina Aganagic, Albrecht Klemm, Marcos Marino +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.AG
paper · pdf · doi:10.1007/s00220-004-1162-z
published as Commun.Math.Phys. 254 (2005) 425-478 · 70 pages, 16 figures, harvmac
arxiv created 2003/06/12 · arxiv updated 2009/11/30
We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric 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 Calabi-Yau. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum 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.