Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instantons on Calabi-Yau and hyper-K\"ahler cones   The instanton equations on vector bundles over Calabi-Yau and hyper-K\"ahler
cones can be reduced to matrix equations resembling Nahm's equations. We
complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau
cones, based on regular semi-simple elements, by a new set of (singular)
boundary conditions which have a known instanton solution in one direction.
This approach extends the classic results of Kronheimer by probing a relation
between generalised Nahm's equations and nilpotent pairs/tuples. Moreover, we
consider quaternionic instantons on hyper-K\"ahler cones over generic
3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up,
using the fact that their analysis can be traced back to the intersection of
three Hermitian Yang-Mills conditions.

14
The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph