The Topological Vertex
Abstract
We 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 Kähler 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.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- March 2005
- DOI:
- 10.1007/s00220-004-1162-z
- arXiv:
- arXiv:hep-th/0305132
- Bibcode:
- 2005CMaPh.254..425A
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Algebraic Geometry
- E-Print:
- 70 pages, 16 figures, harvmac