Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The behavior of sequences of solutions to the Vafa-Witten equations   The Vafa-Witten equations on an oriented Riemannian 4- manifold are first
order, non-linear equations for a pair of connection on a principle SO(3)
bundle over the 4-manifold and a self-dual 2-form with values in the associated
Lie algebra bundle. The main theorem in this paper characterizes in part the
behavior of sequences of solutions to the Vafa-Witten equations which have no
convergent subsequence. The paper proves that a renormalization of a
subsequence of the self-dual 2-form components converges on the complement of a
closed set with Hausdorff dimension at most 2, with the limit being a harmonic
2-form with values in a real line bundle.

26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int