Hidden Symmetries of the Principal Chiral Model Unveiled
C. Devchand, Jeremy Schiff
TL;DR
This paper reveals hidden symmetries in the two-dimensional U(N) Principal Chiral Model by relating it to a linear system, leading to a comprehensive understanding of its symmetries and transformations.
Contribution
It introduces a free-field parametrisation of solutions and uncovers both known and new hidden symmetries of the model.
Findings
All known hidden symmetries are derived from the free-field data.
New symmetries and Bäcklund transformations are identified.
A unified framework for symmetries of the Principal Chiral Model is established.
Abstract
By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all known `hidden symmetries' and B\"acklund transformations, as well as a host of new symmetries, arise.
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