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Topological Open Strings on Orbifolds

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Abstract

We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest. We exemplify this procedure for the \({{\mathbb C}^3/{\mathbb Z}_3}\) orbifold point of local \({{\mathbb P}^2}\), where we present results for topological string amplitudes for genus zero and up to three holes, and for the one-holed torus. These amplitudes can be understood as generating functions for either open orbifold Gromov–Witten invariants of \({{\mathbb C}^3/{\mathbb Z}_3}\), or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators.

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Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, 17 Oxford St., Cambridge, MA, 02138, USA

    Vincent Bouchard

  2. Physikalisches Institut der Universität Bonn, Nußallee 12, D-53115, Bonn, Germany

    Albrecht Klemm

  3. Département de Physique Théorique et Section de Mathématiques, Université de Genève, CH 1211, Genève 4, Switzerland

    Marcos Mariño

  4. Institut de Physique, Université de Neuchâtel, Rue A. L. Breguet 1, CH-2000, Neuchâtel, Switzerland

    Sara Pasquetti

Authors
  1. Vincent Bouchard
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  2. Albrecht Klemm
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  3. Marcos Mariño
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  4. Sara Pasquetti
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Correspondence to Vincent Bouchard.

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Communicated by N.A. Nekrasov

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Bouchard, V., Klemm, A., Mariño, M. et al. Topological Open Strings on Orbifolds. Commun. Math. Phys. 296, 589–623 (2010). https://doi.org/10.1007/s00220-010-1020-0

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