Alladi Ramakrishnan Hall

On a dual to the 2d principal chiral model and its mechanical reduction -- continued

Govind Krishnaswami

CMI, Chennai

The integrable O(4) non-linear sigma model and the closely related
SU(2) principal chiral model (PCM) in 2d serve as toy-models for 4d
Yang-Mills theory as they are asymptotically free and display a mass
gap. Interestingly, the PCM is `dual’ to a scalar field theory that is
strongly coupled in the UV and could serve as a toy-model for theories
with a Landau pole. It is also of interest through connections to the
Wess-Zumino-Witten model and the study of slow light. Unlike the su(2)
current algebra of the PCM, its dual is based on a nilpotent algebra.
Recently, Rajeev and Ranken proposed a mechanical reduction of the
scalar field theory describing certain non-linear waves, whose
quantization survive the passage to the strong-coupling limit. After
placing this model in context, we describe new results on its
Hamiltonian formulation, phase-space structure and classical
integrability, including a Poisson pencil, Lax pairs, classical
r-matrices and a complete set of conserved quantities in involution.
This talk is based on joint work (arXiv:1804.02859) with TR Vishnu.