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Mathematics > Algebraic Geometry

arXiv:1812.05516 (math)
[Submitted on 13 Dec 2018 (v1), last revised 11 Jul 2019 (this version, v4)]

Title:Multiplicative Hitchin Systems and Supersymmetric Gauge Theory

Authors:Chris Elliott, Vasily Pestun
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Abstract:Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra valued. We discuss the relationship between several occurences of these moduli spaces in geometry and supersymmetric gauge theory, with a particular focus on the case where C = CP1 with a fixed framing at infinity. In this case we prove that the identification between multiplicative Higgs bundles and periodic monopoles proved by Charbonneau and Hurtubise can be promoted to an equivalence of hyperkähler spaces, and analyze the twistor rotation for the multiplicative Hitchin system. We also discuss quantization of these moduli spaces, yielding the modules for the Yangian Y(g) discovered by Gerasimov, Kharchev, Lebedev and Oblezin.
Comments: 66 pages. Minor edit correcting a misattributed reference
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA)
Cite as: arXiv:1812.05516 [math.AG]
  (or arXiv:1812.05516v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.05516
Related DOI: https://doi.org/10.1007/s00029-019-0510-y

Submission history

From: Chris Elliott [view email]
[v1] Thu, 13 Dec 2018 16:50:28 UTC (61 KB)
[v2] Sat, 22 Dec 2018 10:20:04 UTC (63 KB)
[v3] Thu, 6 Jun 2019 16:18:15 UTC (76 KB)
[v4] Thu, 11 Jul 2019 08:40:10 UTC (76 KB)
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