Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine View Full Text


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Article Info

DATE

2018-07

AUTHORS

Miranda C. N. Cheng, John F. R. Duncan, Sarah M. Harrison, Jeffrey A. Harvey, Shamit Kachru, Brandon C. Rayhaun

ABSTRACT

We show that certain BPS counting functions for both fundamental strings and strings arising from fivebranes wrapping divisors in Calabi-Yau threefolds naturally give rise to skew-holomorphic Jacobi forms at rational and attractor points in the moduli space of string compactifications. For M5-branes wrapping divisors these are forms of weight negative one, and in the case of multiple M5-branes skew-holomorphic mock Jacobi forms arise. We further find that in simple examples these forms are related to skew-holomorphic (mock) Jacobi forms of weight two that play starring roles in moonshine. We discuss examples involving M5-branes on the complex projective plane, del Pezzo surfaces of degree one, and half-K3 surfaces. For del Pezzo surfaces of degree one and certain half-K3 surfaces we find a corresponding graded (virtual) module for the degree twelve Mathieu group. This suggests a more extensive relationship between Mathieu groups and complex surfaces, and a broader role for M5-branes in the theory of Jacobi forms and moonshine. More... »

PAGES

130

References to SciGraph publications

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  • 2000-02. Calabi–Yau Black Holes and (0,4) Sigma Models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988-02. Jacobi forms and a certain space of modular forms in INVENTIONES MATHEMATICAE
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  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/jhep07(2018)130

    DOI

    http://dx.doi.org/10.1007/jhep07(2018)130

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1105704089


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