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Some boundedness properties of solutions to the Vafa–Witten equations on closed 4-manifolds

Abstract:

We consider a set of gauge-theoretic equations on closed oriented 4-manifolds, which was introduced by Vafa and Witten. The equations involve a triple consisting of a connection and extra fields associated to a principal bundle over a closed oriented 4-manifold. They are similar to Hitchin’s equations over compact Riemann surfaces, and as part of the resemblance, there is no L2-bound on the curvature without an L2-bound on the extra fields. In this article, however, we observe that under the ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1093/qmath/hax015

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Worcester College
Role:
Author
Publisher:
Oxford University Press Publisher's website
Journal:
Quarterly Journal of Mathematics Journal website
Volume:
68
Issue:
4
Pages:
1203-1225
Publication date:
2017-04-12
Acceptance date:
2017-03-02
DOI:
EISSN:
1464-3847
ISSN:
0033-5606
Pubs id:
pubs:794853
URN:
uri:eaeba2d3-25ee-4e4d-9a3e-d8d1828d7631
UUID:
uuid:eaeba2d3-25ee-4e4d-9a3e-d8d1828d7631
Local pid:
pubs:794853
Paper number:
4

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