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Witten’s D 4 integrable hierarchies conjecture

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Abstract

The authors prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D 4 with symmetry group 〈J〉 and for D T4 with symmetry group G max, respectively, are both tau-functions of the D 4 Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof, begun in the article by Fan-Jarvis-Ruan (2013), of the Witten Integrable Hierarchies Conjecture for all simple (ADE) singularities.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Huijun Fan

  2. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    Amanda Francis, Tyler Jarvis & Evan Merrell

  3. Department of Mathematics, University of Michigan Ann Arbor, Michigan, MI, 48105, USA

    Yongbin Ruan

  4. the Yangtz Center of Mathematics at Sichuan University, Chengdu, China

    Yongbin Ruan

Authors
  1. Huijun Fan
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  2. Amanda Francis
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  3. Tyler Jarvis
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  4. Evan Merrell
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  5. Yongbin Ruan
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Corresponding author

Correspondence to Huijun Fan.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11325101, 11271028), the National Security Agency of USA (No.H98230-10-1-0181) and the Doctoral Fund of the Ministry of Education of China (No. 20120001110060).

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Fan, H., Francis, A., Jarvis, T. et al. Witten’s D 4 integrable hierarchies conjecture. Chin. Ann. Math. Ser. B 37, 175–192 (2016). https://doi.org/10.1007/s11401-016-0944-x

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  • DOI: https://doi.org/10.1007/s11401-016-0944-x

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