Title :

Yang–Mills moduli spaces over an orientable closed surface via Fréchet reduction

Author(s) :

Diez, Tobias [Auteur]
Huebschmann, Johannes [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

J.Geom.Phys.

Pages :

393-414

Publication date :

2018

English keyword(s) :

primary
58E15
81T13
secondary
14D20
53C07
58D27
Yang–Mills connection on a closed Riemann surface
Moduli space of smooth Yang–Mills connections on a closed Riemann surface in the Fréchet setting
Stratified symplectic structure on the moduli space of Yang–Mills connections on a closed Riemann surface
Moduli space of holomorphic vector bundles on a projective curve
Fréchet slice analysis

HAL domain(s) :

Physique [physics]/Physique mathématique [math-ph]

English abstract : [en]

Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations ...
Show more >Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure of a Fréchet manifold. Using Wilson loop holonomies and a certain characteristic class determined by the topology of the bundle, we then impose suitable constraints on that Fréchet manifold that single out the based gauge equivalence classes of central Yang–Mills connections but do not directly involve the Yang–Mills equation. We also explain how our theory yields the based and unbased gauge equivalence classes of all Yang–Mills connections and deduce the stratified symplectic structure on the space of unbased gauge equivalence classes of central Yang–Mills connections. The crucial new technical tool is a slice analysis in the Fréchet setting.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL