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Generalised Chern-Simons Theory and G₂-Instantons over Associative Fibrations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Generalised Chern-Simons Theory and G₂-Instantons over Associative Fibrations
Інший ID:
2010 Mathematics Subject Classification: 53C07; 53C38; 58J28
DOI:10.3842/SIGMA.2014.083
DOI:10.3842/SIGMA.2014.083
Посилання:
Generalised Chern-Simons Theory and G₂-Instantons over Associative Fibrations / Henrique N. Sá Earp // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 18 назв. — англ.
Підтримка:
The author thanks Simon Donaldson for suggesting the matter of this paper, Thomas Walpuski
for sharing some unpublished notes and Marcos Jardim for several useful discussions. Special
thanks also to the anonymous referees for numerous mathematical and reference contributions.
Дата:
2014
Переглядів:
503
Завантажень:
186
Анотація:
Adjusting conventional Chern-Simons theory to G₂-manifolds, one describes G₂-instantons on bundles over a certain class of 7-dimensional flat tori which fiber non-trivially over T⁴, by a pullback argument. Moreover, if c₂≠0, any (generic) deformation of the G₂-structure away from such a fibred structure causes all instantons to vanish. A brief investigation in the general context of (conformally compatible) associative fibrations f:Y⁷→X⁴ relates G₂-instantons on pullback bundles f∗E→Y and self-dual connections on the bundle E→X over the base, a fact which may be of independent interest.
