English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We revisit Vafa-Witten theory in the more general setting whereby theunderlying moduli space is not that of instantons, but of the full Vafa-Wittenequations. We physically derive (i) a novel Vafa-Witten four-manifold invariantassociated with this moduli space, (ii) their relation to Gromov-Witteninvariants, (iii) a novel Vafa-Witten Floer homology assigned to three-manifoldboundaries, (iv) a novel Vafa-Witten Atiyah-Floer correspondence, (v) a proofand generalization of a conjecture by Abouzaid-Manolescu in [1] about thehypercohomology of a perverse sheaf of vanishing cycles, (vi) a Langlandsduality of these invariants, Floer homologies and hypercohomology, and (vii) aquantum geometric Langlands correspondence with purely imaginary parameter thatspecializes to the classical correspondence in the zero-coupling limit, whereHiggs bundles feature in (ii), (iv), (vi) and (vii). We also explain how theseinvariants and homologies will be categorified in the process, and discusstheir higher categorification. We therefore relate differential and enumerativegeometry, topology and geometric representation theory in mathematics, via amaximally-supersymmetric topological quantum field theory withelectric-magnetic duality in physics.

Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification