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Refined stable pair invariants for E-, M- and [p, q]-strings

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Abstract

We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces and elliptic surfaces, in particular the half K3. The BPS numbers contribute naturally to the fivedimensional N =1 supersymmetric index of M-theory, but they can be also interpreted in terms of the superconformal index in six dimensions and upon dimensional reduction the generating functions count N = 2 Seiberg-Witten gauge theory instantons in four dimensions. Using the M/F-theory uplift the additional information encoded in the spin content can be used in an essential way to obtain information about BPS states in physical systems associated to small instantons, tensionless strings, gauge symmetry enhancement in F-theory by [p, q]-strings as well as M-strings.

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  1. Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Min-xin Huang

  2. Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany

    Albrecht Klemm & Maximilian Poretschkin

  3. Hausdorff Center for Mathematics, Universität Bonn, D-53115, Bonn, Germany

    Albrecht Klemm

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  1. Min-xin Huang
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Huang, Mx., Klemm, A. & Poretschkin, M. Refined stable pair invariants for E-, M- and [p, q]-strings. J. High Energ. Phys. 2013, 112 (2013). https://doi.org/10.1007/JHEP11(2013)112

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