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The Topological Vertex

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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.

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Author information

Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA

    Mina Aganagic & Cumrun Vafa

  2. Institut für Physik, Humboldt-Universität zu Berlin, 10115, Berlin, Germany

    Albrecht Klemm

  3. Theory Division, CERN, Geneva 23, 1211, Switzerland

    Marcos Mariño

  4. California Institute of Technology, 452-48, Pasadena, CA, 91125, USA

    Cumrun Vafa

Authors
  1. Mina Aganagic
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  2. Albrecht Klemm
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  3. Marcos Mariño
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  4. Cumrun Vafa
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Additional information

Communicated by N. Nekrasov

Acknowledgement We would like to thank D.-E.Diaconescu, R. Dijkgraaf, J. Gomis, A. Grassi, A. Iqbal, A. Kapustin, S. Katz, V. Kazakov, I. Kostov, C-C. Liu, H. Ooguri, J. Schwarz, S. Shenker and E. Zaslow for valuable discussions (and the cap!). The research of MA and CV was supported in part by NSF grants PHY-9802709 and DMS-0074329. In addition, CV thanks the hospitality of the theory group at Caltech, where he is a Gordon Moore Distinguished Scholar. M.A. is grateful to the Caltech theory group for hospitality during part of this work. A.K. is supported in part by the DFG grant KL-1070/2-1.

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Aganagic, M., Klemm, A., Mariño, M. et al. The Topological Vertex. Commun. Math. Phys. 254, 425–478 (2005). https://doi.org/10.1007/s00220-004-1162-z

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