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Perturbative Corrections to Kähler Moduli Spaces

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Abstract

We propose a general formula for perturbative-in-α′ corrections to the Kähler potential on the quantum Kähler moduli space of Calabi–Yau n-folds, for any n, in their asymptotic large volume regime. The knowledge of such perturbative corrections provides an important ingredient needed to analyze the full structure of this Kähler potential, including nonperturbative corrections such as the Gromov–Witten invariants of the Calabi–Yau n-folds. We argue that the perturbative corrections take a universal form, and we find that this form is encapsulated in a specific additive characteristic class of the Calabi–Yau n-fold which we call the log Gamma class, and which arises naturally in a generalization of Mukai’s modified Chern character map. Our proposal is inspired heavily by the recent observation of an equality between the partition function of certain supersymmetric, two-dimensional gauge theories on a two-sphere, and the aforementioned Kähler potential. We further strengthen our proposal by comparing our findings on the quantum Kähler moduli space to the complex structure moduli space of the corresponding mirror Calabi–Yau geometry.

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Authors and Affiliations

  1. KITP, University of California, Santa Barbara, CA, 93106, USA

    James Halverson

  2. Bethe Center for Theoretical Physics, Physikalisches Institut, Universität Bonn, 53115, Bonn, Germany

    Hans Jockers

  3. Department of Physics, McGill University, Montreal, QC, Canada

    Joshua M. Lapan

  4. Departments of Mathematics and Physics, University of California, Santa Barbara, CA, 93106, USA

    David R. Morrison

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  1. James Halverson
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  2. Hans Jockers
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  4. David R. Morrison
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Correspondence to Hans Jockers.

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Communicated by H.-T. Yau

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Halverson, J., Jockers, H., Lapan, J.M. et al. Perturbative Corrections to Kähler Moduli Spaces. Commun. Math. Phys. 333, 1563–1584 (2015). https://doi.org/10.1007/s00220-014-2157-z

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