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SUMMARY:Quantum gauge theories and integrable systems (2/4)
DTSTART;VALUE=DATE-TIME:20141014T123000Z
DTEND;VALUE=DATE-TIME:20141014T143000Z
DTSTAMP;VALUE=DATE-TIME:20220810T114611Z
UID:indico-event-570@indico.math.cnrs.fr
DESCRIPTION:Seiberg-Witten theory maps supersymmetric four-dimensional gau
ge theories with extended supersymmetry to algebraic completely integrab
le systems. For large class of such integrable systems the phase space is
the moduli space of solutions of self-dual hyperKahler equations and their
low-dimensional descendants. In particular\, the list of such integrable
systems includes Hitchin systems defined on Riemann surfaces with singular
ities 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 hyperKahler manifolds (four-dimensional P
DE or elliptically valued Hitchin system). Deformations of four-dimensiona
l gauge theory by curved backgrounds correspond to the quantization of the
associated algebraic integrable systems. Quantization of Hitchin systems
has relation to geometric Langlands correspondence and to the Toda two-dim
ensional conformal theory with Wg-algebra symmetry. Quantization of g-mono
pole and g-instanton moduli spaces relates to the representation theory of
Drinfeld-Jimbo quantum affine algebras (and their rational and elliptic v
ersions\, 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 case (elliptically valued Hitchin).
It is expected that there exists an analogue of geometric Langlands corre
spondence for quantization of the monopole and instanton algebraic integra
ble system (circle-valued and elliptically-valued Hitchin).\n\nhttps://ind
ico.math.cnrs.fr/event/570/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/570/
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