https://doi.org/10.1140/epjc/s10052-022-10553-0
Regular Article - Theoretical Physics
2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles
1
Institute of Theoretical and Experimental Physics, NRCKI, B. Cheremushkinskaya, 25, 117259, Moscow, Russia
2
Institute for Information Transmission Problems RAS (Kharkevich Institute), Bolshoy Karetny per. 19, 127994, Moscow, Russia
3
National Research University Higher School of Economics, Russian Federation, Usacheva str. 6, 119048, Moscow, Russia
4
Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia
Received:
12
April
2022
Accepted:
26
June
2022
Published online:
23
July
2022
We compare the construction of 2D integrable models through two gauge field theories. The first one is the 4D Chern–Simons (4D-CS) theory proposed by Costello and Yamazaki. The second one is the 2D generalization of the Hitchin integrable systems constructed by means of affine Higgs bundles (AHB). We illustrate the latter approach by considering 1 + 1 field versions of integrable systems including the Calogero–Moser field theory, the Landau–Lifshitz model and the field theory generalization of the elliptic Gaudin model.
© The Author(s) 2022
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