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arXiv · 1401.5462

Generalised Chern-Simons Theory and ${\rm G}_2$-Instantons over Associative Fibrations

Henrique N. Sá Earp
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Abstract

Adjusting conventional Chern-Simons theory to ${\rm G}_2$-manifolds, one describes ${\rm G}_2$-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 ${\rm G}_2$-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 ${\rm G}_2$-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.

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BibTeXRIS

Henrique N. Sá Earp. 2014-01-21. Generalised Chern-Simons Theory and ${\rm G}_2$-Instantons over Associative Fibrations. https://doi.org/10.3842/sigma.2014.083

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