2020
Calvo-Andrade, Omegar; Díaz, Lázaro O. Rodríguez; Earp, Henrique N. Sá
Gauge theory and G2-geometry on Calabi–Yau links Journal Article
Em: Revista Matemática Iberoamericana, vol. 36, iss. 6, pp. 1753–1778, 2020.
Resumo | Links | BibTeX | Tags: Gauge Theory
@article{nokey,
title = {Gauge theory and G2-geometry on Calabi\textendashYau links},
author = {Omegar Calvo-Andrade and L\'{a}zaro O. Rodr\'{i}guez D\'{i}az and Henrique N. S\'{a} Earp},
doi = {http://dx.doi.org/10.4171/rmi/1182},
year = {2020},
date = {2020-02-21},
journal = {Revista Matem\'{a}tica Iberoamericana},
volume = {36},
issue = {6},
pages = {1753\textendash1778},
abstract = {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-closed G2-structure φ induced by the Calabi-Yau 3-orbifold basic geometry. We distinguish these pairs (K,φ) by the Crowley-Nordstr\"{o}m 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.},
keywords = {Gauge Theory},
pubstate = {published},
tppubtype = {article}
}
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-closed 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.
2017
Jardim, Marcos; Menet, Grégoire; Prata, Daniela M.; Earp, Henrique N. Sá
Holomorphic bundles for higher dimensional gauge theory Journal Article
Em: Bulletin of the London Mathematical Society, vol. 49, iss. 1, pp. 117-132, 2017.
Resumo | Links | BibTeX | Tags: Gauge Theory
@article{nokey,
title = {Holomorphic bundles for higher dimensional gauge theory},
author = {Marcos Jardim and Gr\'{e}goire Menet and Daniela M. Prata and Henrique N. S\'{a} Earp},
url = {https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms.12017},
doi = {https://doi.org/10.1112/blms.12017},
year = {2017},
date = {2017-01-17},
urldate = {2017-01-17},
journal = {Bulletin of the London Mathematical Society},
volume = {49},
issue = {1},
pages = {117-132},
abstract = {Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non-compact 3-folds, called building blocks, satisfying a stability condition ‘at infinity’. Such bundles are known to parametrize solutions of the Yang\textendashMills equation over the -manifolds obtained from asymptotically cylindrical Calabi\textendashYau 3-folds studied by Kovalev, Haskins et al. and Corti et al. The most important tool is a generalization of Hoppe's stability criterion to holomorphic bundles over smooth projective varieties with , a result which may be of independent interest. Finally, we apply monads to produce a prototypical model of the curvature blow-up phenomenon along a sequence of asymptotically stable bundles degenerating into a torsion-free sheaf.},
keywords = {Gauge Theory},
pubstate = {published},
tppubtype = {article}
}
Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non-compact 3-folds, called building blocks, satisfying a stability condition ‘at infinity’. Such bundles are known to parametrize solutions of the Yang–Mills equation over the -manifolds obtained from asymptotically cylindrical Calabi–Yau 3-folds studied by Kovalev, Haskins et al. and Corti et al. The most important tool is a generalization of Hoppe's stability criterion to holomorphic bundles over smooth projective varieties with , a result which may be of independent interest. Finally, we apply monads to produce a prototypical model of the curvature blow-up phenomenon along a sequence of asymptotically stable bundles degenerating into a torsion-free sheaf.