Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Families of solutions of the heterotic G$_2$ system   We construct new families of solutions of the heterotic G$_2$ system on
squashed homogeneous 3-Sasakian manifolds, that is, using squashed metrics on
either the 7-sphere or the Aloff-Wallach space $N_{1,1}$. We obtain AdS$_3$
solutions for all values of the squashing parameter $s$ except for the
nearly-parallel G$_2$ value $s=1/\sqrt{5}$, for which we don't find any
solutions. Along the process, we construct different G$_2$-instanton
connections on bundles over these squashed manifolds.

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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat