Abstract
In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in [1] 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.
Highlights
There are at least three major characteristics present in any lambda model suggesting a relation with a gauge theory of the CS type:
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
Summary
We collect some relevant results of the lambda deformed PCM that will facilitate its identification as the reduced field theory obtained by performing a SR on an holomorphic CS theory . All the results can be found in the literature and are briefly gathered here in order to maintain the text self-contained. The only relatively new detail concerns a differential ω constructed out of the twist function φ of the theory that will play a prominent role in the holomorphic CS theory considered in (3)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
