Gauge theory and G(2)-geometry on Calabi-Yau links

Autor(es)

Calvo-Andrade, Omegar ^[1] ; Rodriguez Diaz, Lazaro O. ^[2] ; Sa Earp, Henrique N. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: REVISTA MATEMATICA IBEROAMERICANA; v. 36, n. 6, p. 1753-1778, 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/24727-0 - G2-instantons sobre somas conexas torcidas
• Beneficiário: Henrique Nogueira de Sá Earp
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/13357-7 - O complexo quiral de de Rham em variedades com holonomia Spin (7)
• Beneficiário: Lazaro Orlando Rodriguez Diaz
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 14/23594-6 - Folheações holomorfas cujo feixe tangente é localmente livre
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional