Supersymmetric Yang-Mills theory on contact Calabi-Yau 7-manifolds
Geometric flows of G2-structures, and their Yang-Mills connections.
| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] CIMAT, Apartado Postal 402, Guanajuato 36000, Guanajuato - Mexico
[2] Univ Fed Rio de Janeiro, IM, Ctr Tecnol, Av Athos da Silveira Ramos 149, Bloco C, BR-21941909 Rio de Janeiro, RJ - Brazil
[3] Univ Estadual Campinas, IMECC, Rua Sergio Buarque de Holanda, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | REVISTA MATEMATICA IBEROAMERICANA; v. 36, n. 6, p. 1753-1778, 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
The 7-dimensional link K of a weighted homogeneous hyper-surface on the round 9-sphere in C-5 has a nontrivial null Sasakian structure which is contact Calabi-Yau, in many cases. It admits a canonical co-calibrated G(2)-structure phi induced by the Calabi-Yau 3-orbifold basic geometry. We distinguish these pairs (K, phi) by the Crowley-Nordstrom Z(48)-valued nu 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 G(2)-instantons on holomorphic Sasakian bundles over K are exactly the transversely Hermitian Yang-Mills connections. As a proof of principle, we obtain G(2)-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 G(2)-instanton count. (AU) | |
| FAPESP's process: | 14/24727-0 - G2-instantons over twisted connected sums |
| Grantee: | Henrique Nogueira de Sá Earp |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 14/13357-7 - Chiral de Rham complex in manifolds with holonomy Spin(7) |
| Grantee: | Lazaro Orlando Rodriguez Diaz |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 14/23594-6 - Holomorphic foliations with locally free tangent sheaf |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |