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Type II/F-theory superpotentials with several deformations and \( \mathcal{N} = 1 \) mirror symmetry

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Abstract

We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the off-shell superpotential and its analytic properties under deformation. Explicit expressions for the \( \mathcal{N} = 1 \) superpotential for families of type II/F-theory compactifications are obtained for a list of multi-parameter examples. Using the Hodge theoretic approach to open-string mirror symmetry, we obtain new predictions for integral disc invariants in the A model instanton expansion. We study the behavior of the brane vacua under extremal transitions between different Calabi-Yau spaces and observe that the web of Calabi-Yau vacua remains connected for a particular class of branes.

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Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, U.S.A.

    Murad Alim

  2. Arnold Sommerfeld Center for Theoretical Physics, LMU, Theresienstr. 37, D-80333, Munich, Germany

    Michael Hecht, Peter Mayr, Adrian Mertens & Masoud Soroush

  3. Department of Physics, Stanford University, Stanford, CA, 94305–4060, U.S.A.

    Hans Jockers

  4. Kavli Institute for Theoretical Physics, Santa Barbara, CA, 93106, U.S.A.

    Hans Jockers

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  1. Murad Alim
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  2. Michael Hecht
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Correspondence to Peter Mayr.

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Alim, M., Hecht, M., Jockers, H. et al. Type II/F-theory superpotentials with several deformations and \( \mathcal{N} = 1 \) mirror symmetry. J. High Energ. Phys. 2011, 103 (2011). https://doi.org/10.1007/JHEP06(2011)103

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