Abstract
AbstractWe derive the $$2\hbox {d}$$
2
d
Zakharov–Mikhailov action from $$4\hbox {d}$$
4
d
Chern–Simons theory. This $$2\hbox {d}$$
2
d
action is known to produce as equations of motion the flatness condition of a large class of Lax connections of Zakharov–Shabat type, which includes an ultralocal variant of the principal chiral model as a special case. At the $$2\hbox {d}$$
2
d
level, we determine for the first time the covariant Poisson bracket r-matrix structure of the Zakharov–Shabat Lax connection, which is of rational type. The flatness condition is then derived as a covariant Hamilton equation. We obtain a remarkable formula for the covariant Hamiltonian in terms of the Lax connection which is the covariant analogue of the well-known formula “$$H={{\,\mathrm{Tr}\,}}L^2$$
H
=
Tr
L
2
”.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference35 articles.
1. Affleck, I., Bykov, D., Wamer, K.: Flag manifold sigma models: spin chains and integrable theories. arXiv:2101.11638
2. Appadu, C., Hollowood, T.J., Price, D.: Quantum inverse scattering and the Lambda deformed principal chiral model. J. Phys. A 50(30), 305401 (2017). arXiv:1703.06699
3. Benini, M., Schenkel, A., Vicedo, B.: Homotopical analysis of 4d Chern–Simons theory and integrable field theories. arXiv:2008.01829
4. Bykov, D.: Flag manifold Sigma models and Nilpotent orbits. Proc. Steklov Inst. Math. 309, 78–86 (2020)
5. Bykov, D.: Quantum flag manifold $$\sigma $$-models and Hermitian Ricci flow. arXiv:2006.14124
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献