Gauge theory and G2-geometry on Calabi–Yau links

• Omegar Calvo-Andrade ^[1] ; Lázaro O. Rodríguez Díaz ^[2] ; Henrique N. Sá Earp ^[3]
  1. [1] Mathematics Research Center

     Mathematics Research Center

     México

     
  2. [2] Universidade Federal do Rio de Janeiro

     Universidade Federal do Rio de Janeiro

     Brasil

     
  3. [3] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 6, 2020, págs. 1753-1778
• Idioma: inglés
• DOI: 10.4171/rmi/1182
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• Resumen

  • The 7-dimensional link K of a weighted homogeneous hypersurface on the round 9-sphere in C5 has a nontrivial null Sasakian structure which is contact Calabi–Yau, in many cases. It admits a canonical co-calibrated G2-structure φ induced by the Calabi–Yau 3-orbifold basic geometry. We distinguish these pairs (K,φ) by the Crowley–Nordström Z48-valued ν invariant, for which we prove odd parity and provide an algorithmic formula.

    We describe moreover a natural Yang–Mills theory on such spaces, with many important features of the torsion-free case, such as a Chern–Simons formalism and topological energy bounds. In fact, compatible G2-instantons on holomorphic Sasakian bundles over K are exactly the transversely Hermitian Yang–Mills connections. As a proof of principle, we obtain G2-instantons over the Fermat quintic link from stable bundles over the smooth projective Fermat quintic, thus relating in a concrete example the Donaldson–Thomas theory of the quintic threefold with a conjectural G2-instanton count.