Holomorphic Chern-Simons theory and lambda models: PCM case

Abstract

In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in arXiv:1908.02289 for describing integrable field theories. We work out explicitly the case of the lambda deformed Principal Chiral Model (PCM) and show that the symplectic reduction works as a localization mechanism. The reduced Chern-Simons theory restricts to the set of poles of the twist function underlying the theory, where the known classical integrability of the lambda deformed PCM can be reconstructed from the phase space data associated to this set of points in the spectral space.

arXiv commentPublished version

References in corpus (15)

• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Integrable Deformations of Strings on Symmetric Spaces
• The all-loop non-Abelian Thirring model and its RG flow
• On a `universal' class of WZW-type conformal models
• Integrable Lambda Models And Chern-Simons Theories
• Exploring The Lambda Model Of The Hybrid Superstring
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Giant Magnons of String Theory in the Lambda Background
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Integrable Generalized Thirring Model
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring

Cited by in corpus (12)

• 4-dimensional Chern-Simons theory and integrable field theories
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• 4D Chern-Simons theory with auxiliary fields
• The Courant-Hilbert construction in 4D Chern-Simons theory
• 3-dimensional mixed BF theory and Hitchin's integrable system
• A generalized 4d Chern-Simons theory