| Full text | |
| Author(s): |
Portilla, Luis E.
;
Sa Earp, Henrique N.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | QUARTERLY JOURNAL OF MATHEMATICS; v. N/A, p. 57-pg., 2023-03-28. |
| Abstract | |
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) | |
| FAPESP's process: | 17/20007-0 - Gauge theory and geometric structures in dimension 7 |
| Grantee: | Henrique Nogueira de Sá Earp |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/21391-1 - Gauge theory and algebraic geometry |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Projects - Thematic Grants |