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SUMMARY:Quantum gauge theories and integrable systems (4/4)
DTSTART;VALUE=DATE-TIME:20141028T133000Z
DTEND;VALUE=DATE-TIME:20141028T153000Z
DTSTAMP;VALUE=DATE-TIME:20221001T183800Z
UID:indico-event-572@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vasily PESTUN (IHES)\n\nSeiberg-Witten theory maps s
upersymmetric four-dimensional gauge theories with extended supersymmetry
to algebraic completely integrable systems. For large class of such inte
grable systems the phase space is the moduli space of solutions of self-du
al hyperKahler equations and their low-dimensional descendants. In particu
lar\, the list of such integrable systems includes Hitchin systems defined
on Riemann surfaces with singularities at marked points (two-dimensional
PDE)\, monopoles on circle bundles over surfaces (three-dimensional PDE or
circle-valued Hitchin system) and instantons on torically fibered hyperKa
hler manifolds (four-dimensional PDE or elliptically valued Hitchin system
). Deformations of four-dimensional gauge theory by curved backgrounds cor
respond to the quantization of the associated algebraic integrable systems
. Quantization of Hitchin systems has relation to geometric Langlands corr
espondence and to the Toda two-dimensional conformal theory with Wg-algebr
a symmetry. Quantization of g-monopole and g-instanton moduli spaces relat
es to the representation theory of Drinfeld-Jimbo quantum affine algebras
(and their rational and elliptic versions\, Yangians and elliptic groups)\
, associated respectively to g in the monopole case (circle-valued Hitchin
) and to the central extension of the loop algebra of g in the instanton c
ase (elliptically valued Hitchin). It is expected that there exists an ana
logue of geometric Langlands correspondence for quantization of the monopo
le and instanton algebraic integrable system (circle-valued and elliptical
ly-valued Hitchin).\n\nhttps://indico.math.cnrs.fr/event/572/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/572/
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