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Monopoles and Four-Manifolds
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abstract
Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$ instantons, one can define equivalent four-manifold invariants by counting solutions of a non-linear equation with an abelian gauge group. This is a ``dual'' equation in which the gauge group is the dual of the maximal torus of $SU(2)$. The new viewpoint suggests many new results about the Donaldson invariants.
Forward citations
Cited by 4 Pith papers
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Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories
For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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Refined Vafa-Witten invariants for toric surfaces from supersymmetric localization in 5D gauge theory
5D N=1* supersymmetric localization on toric surfaces equals refined Vafa–Witten invariants for odd first Chern class; the even-c1 case fails without a hand-added constant.
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A survey of knots and quivers
This is a review of knot polynomials, triply-graded knot homologies, and the knots-quivers correspondence, with no new results.
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