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Communications in Mathematical Physics

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

The Topological Vertex

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

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.

Keywords

Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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