Communications in Mathematical Physics

, Volume 254, Issue 2, pp 425–478 | Cite as

The Topological Vertex

  • Mina Aganagic
  • Albrecht Klemm
  • Marcos Mariño
  • Cumrun Vafa


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.


Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mina Aganagic
    • 1
  • Albrecht Klemm
    • 2
  • Marcos Mariño
    • 3
  • Cumrun Vafa
    • 1
    • 4
  1. 1.Jefferson Physical LaboratoryHarvard UniversityCambridgeUSA
  2. 2.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Theory DivisionCERNSwitzerland
  4. 4.California Institute of TechnologyPasadenaUSA

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