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On flux quantization in F-theory

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Abstract

We study the problem of four-form flux quantization in F-theory compactifications. We prove that for smooth, elliptically fibered Calabi-Yau fourfolds with a Weierstrass representation, the flux is always integrally quantized. This implies that any possible half- integral quantization effects must come from 7-branes, i.e. from singularities of the fourfold.

We subsequently analyze the quantization rule on explicit fourfolds with Sp(N) singularities, and connect our findings via Sen’s limit to IIB string theory. Via direct computations we find that the four-form is half-integrally quantized whenever the corresponding 7-brane stacks wrap non-spin complex surfaces, in accordance with the perturbative Freed-Witten anomaly. Our calculations on the fourfolds are done via toric techniques, whereas in IIB we rely on Sen’s tachyon condensation picture to treat bound states of branes. Finally, we give general formulae for the curvature- and flux-induced D3 tadpoles for general fourfolds with Sp(N) singularities.

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Authors and Affiliations

  1. Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333, München, Germany

    Andrés Collinucci

  2. Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, WI, 53706-1390, USA

    Raffaele Savelli

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  1. Andrés Collinucci
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  2. Raffaele Savelli
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Correspondence to Andrés Collinucci.

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Collinucci, A., Savelli, R. On flux quantization in F-theory. J. High Energ. Phys. 2012, 15 (2012). https://doi.org/10.1007/JHEP02(2012)015

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