Master spaces and the coupling principle: from Geometric Invariant Theory to Gauge Theory

Andrei Teleman (1) , Christian Okonek (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Institut für Mathematik [Zürich]

We introduce a general mathematical principle, with roots in Geometric Invariant Theory, which provides a unified way for understanding several celebrated results and conjectures like e. g. the Verlinde formula, the Vafa-Intriligator formula, and Witten's conjecture about the relation between Donaldson theory and Seiberg-Witten theory. This principle also suggests new results about Gromov invariants of moduli spaces of stable bundles over curves, and shows that gauge theoretical invariants associated with moduli spaces of PU(2)-monopoles are determined by Seiberg-Witten and Donaldson invariants.

Mots clés: Geometric Invariant Theory; Gauge Theory; Master Space; localization

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Andrei Teleman, Christian Okonek. Master spaces and the coupling principle: from Geometric Invariant Theory to Gauge Theory. Communications in Mathematical Physics, 1999, 205 (2), pp.437-458. ⟨10.1007/s002200050685⟩. ⟨hal-00881759⟩