Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Limit of Large Mass Monopoles   In this paper we consider $\rm SU(2)$ monopoles on an asymptotically conical,
oriented, Riemannian $3$-manifold with one end. The connected components of the
moduli space of monopoles in this setting are labeled by an integer called the
charge. We analyse the limiting behavior of sequences of monopoles with fixed
charge, and whose sequence of Yang--Mills--Higgs energies is unbounded. We
prove that the limiting behavior of such monopoles is characterized by energy
concentration along a certain set, which we call the blow-up set. Our work
shows that this set is finite, and using a bubbling analysis obtain effective
bounds on its cardinality, with such bounds depending solely on the charge of
the monopole. Moreover, for such sequences of monopoles there is another
naturally associated set, the zero set, which consists on the set at which the
zeros of the Higgs fields accumulate. Regarding this, our results show that for
such sequences of monopoles, the zero set and the blow-up set coincide. In
particular, proving that in this "large mass" limit, the zero set is a finite
set of points. Some of our work extends for sequences of finite mass critical
points of the Yang--Mills--Higgs functional for which the Yang--Mills--Higgs
energies are $O(m_i)$ as $i\to\infty$, where $m_i$ are the masses of the
configurations.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat