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Generalised Chern–Simons Theory and $\mathrm{G}_2$-Instantons over Associative Fibrations
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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Adjusting conventional Chern–Simons theory to $\mathrm{G}_2$-manifolds, one describes $\mathrm{G}_2$-instantons on bundles over a certain class of $7$-dimensional flat tori which fiber non-trivially over $T^4$, by a pullback argument. Moreover, if $c_2\neq0$, any (generic) deformation of the $\mathrm{G}_2$-structure away from such a fibred structure causes all instantons to vanish. A brief investigation in the general context of (conformally compatible) associative fibrations $f:Y^7\to X^4$ relates $\mathrm{G}_2$-instantons on pullback bundles $f^*E\to Y$ and self-dual connections on the bundle $E\to X$ over the base, a fact which may be of independent interest.
Keywords: Chern–Simons; Yang–Mills; $\mathrm{G}_2$-manifolds; associative fibrations. 
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     title = {Generalised {Chern{\textendash}Simons} {Theory} and $\mathrm{G}_2${-Instantons} over {Associative} {Fibrations}},
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Henrique N. Sá Earp. Generalised Chern–Simons Theory and $\mathrm{G}_2$-Instantons over Associative Fibrations. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a82/

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