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I recently came across a paper of Witten that talks about the S-matrix of the supersymmetric non-linear sigma model. In the beginning part of the paper, he mentions that theories like the non-linear sigma model or the sine-gordon theory have an infinite number of conserved charges which come from locally conserved currents. Also, that the sine-gordon theory which is given by

$${L=\frac{1}{2}\partial_{\mu}\varphi \partial^{\mu}\varphi+\frac{m^2}{\beta^2}cos(\beta \varphi)}$$ supposedly has a conserved charge in every representation of the Lorentz group.

I don't understand how this comes about. It would be great if someone could help me with figuring out how to construct higher spin conserved charges.

This is the paper: https://doi.org/10.1103/PhysRevD.17.2134

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  • $\begingroup$ This seems relevant: arxiv.org/abs/0707.1603 $\endgroup$
    – Qmechanic ♦
    Jul 17, 2022 at 13:14
  • $\begingroup$ This is shown in Takhtadzhyan, L. A., & Faddeev, L. D. (1974). Essentially nonlinear one-dimensional model of classical field theory. Theoretical and Mathematical Physics, 21(2), 1046–1057. doi:10.1007/bf01035551, by the method that later came to be known as The algebraic Bethe Ansatz or Quantum inverse scattering method. $\endgroup$
    – Rebour
    Oct 14, 2022 at 18:53

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