Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Brief Survey of Higgs Bundles   Considering a compact Riemann surface of genus greater than two, a
Higgs~bundle is a pair composed of a holomorphic bundle over the Riemann
surface, joint with an auxiliar vector field, so-called Higgs field. This
theory started around thirty years ago, with Hitchin's work, when he reduced
the self-duality equations from dimension four to dimension two, and so,
studied those equations over Riemann surfaces. Hitchin baptized those fields as
"Higgs fields" beacuse in the context of physics and gauge theory, they
describe similar particles to those described by the Higgs bosson. Later,
Simpson used the name "Higgs bundle" for a holomorphic bundle together with a
Higgs field. Today, Higgs bundles are the subject of research in several areas
such as non-abelian Hodge theory, Langlands, mirror symmetry, integrable
systems, quantum field theory (QFT), among others. The main purposes here are
to introduce these objects, and to present a brief construction of the moduli
space of Higgs bundles.

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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph