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Anomaly cancellation and modularity, II: The E 8 ×E 8 case

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Abstract

In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group E 8 × E 8 and the Hořava-Witten anomaly factorization formula for the gauge group E8 can be derived through modular forms of weight 14. This answers a question of Schwarz. We also establish generalizations of these factorization formulas and obtain a new Hořava-Witten type factorization formula.

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Acknowledgements

This work was supported by a start-up grant from National University of Singapore (Grant No. R-146-000-132-133), National Science Foundation of USA (Grant No. DMS-1510216) and National Natural Science Foundation of China (Grant No. 11221091). The authors are indebted to J. H. Schwarz for asking them the question considered in this paper. The authors also thank Siye Wu for helpful and inspiring communications.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, 119076, Singapore

    Fei Han

  2. Department of Mathematics, Capital Normal University, Beijing, 100048, China

    KeFeng Liu

  3. Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, 90095, USA

    KeFeng Liu

  4. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, 300071, China

    WeiPing Zhang

Authors
  1. Fei Han
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  2. KeFeng Liu
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  3. WeiPing Zhang
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Correspondence to WeiPing Zhang.

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In memory of Professor LU QiKeng (1927–2015)

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Han, F., Liu, K. & Zhang, W. Anomaly cancellation and modularity, II: The E 8 ×E 8 case. Sci. China Math. 60, 985–994 (2017). https://doi.org/10.1007/s11425-016-9034-1

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  • DOI: https://doi.org/10.1007/s11425-016-9034-1

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