Instantons on Sasakian 7-manifolds

Autor(es)

Portilla, Luis E. ; Sa Earp, Henrique N.

• Tipo de documento: Artigo Científico
• Fonte: QUARTERLY JOURNAL OF MATHEMATICS; v. N/A, p. 57-pg., 2023-03-28.

Resumo

We study a natural contact instanton equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related to both the transverse Hermitian Yang-Mills (HYM) condition and the G(2)-instanton equation. We obtain, by Fredholm theory, a finite-dimensional local model for the moduli space of irreducible solutions. Following the approach by Baraglia and Hekmati in five dimensions [], we derive cohomological conditions for smoothness and express its dimension in terms of the index of a transverse elliptic operator. Finally, we show that the moduli space of self-dual contact instantons is Kahler, in the Sasakian case. As an instance of concrete interest, we specialize to transversely holomorphic Sasakian bundles over contact Calabi-Yau 7-manifolds, as studied by Calvo-Andrade, Rodriguez and Sa Earp [], and we show that in this context the notions of contact instanton, integrable G(2)-instanton and HYM connection coincide. (AU)

• Processo FAPESP: 17/20007-0 - Teoria de calibres e estruturas geométricas em dimensão 7
• Beneficiário: Henrique Nogueira de Sá Earp
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/21391-1 - Teoria de calibre e geometria algébrica
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Temático