Integrable deformations of coupled σ-models
Open Access
- 13 May 2020
- journal article
- research article
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (5) , 1-59
Abstract
We construct integrability-preserving deformations of the integrable σ-model coupling together N copies of the Principal Chiral Model. These deformed theories are obtained using the formalism of affine Gaudin models, by applying various combinations of Yang-Baxter and λ-deformations to the different copies of the undeformed model. We describe these models both in the Hamiltonian and Lagrangian formulation and give explicit expressions of their action and Lax pair. In particular, we recover through this construction various integrable λ-deformed models previously introduced in the literature. Finally, we discuss the relation of the present work with the semi-homolomorphic four-dimensional Chern-Simons theory.Keywords
All Related Versions
This publication has 64 references indexed in Scilit:
- Non-abelian duality and canonical transformationsPhysics Letters B, 1995
- Dual non-Abelian duality and the Drinfeld doublePhysics Letters B, 1995
- A new family of SU(2) symmetric integrable sigma modelsPhysics Letters B, 1994
- On the classical origins of yangian symmetry in integrable field theoryPhysics Letters B, 1992
- Hamiltonian structures for integrable classical theories from graded Kac-Moody algebrasPhysics Letters B, 1986
- Kac-Moody algebra and extended Yang-Baxter relations in the O(N) non-linear σ-modelPhysics Letters B, 1985
- Non-abelian bosonization in two dimensionsCommunications in Mathematical Physics, 1984
- The Hamiltonian formalism and a many-valued analogue of Morse theoryRussian Mathematical Surveys, 1982
- Relativistically invariant quasiclassical limits of integrable two-dimensional quantum modelsTheoretical and Mathematical Physics, 1981
- Consequences of anomalous ward identitiesPhysics Letters B, 1971