An action variable of the sine-Gordon model

TL;DR

This paper explores an action variable in the sine-Gordon model, relating it to Bäcklund transformations and hidden symmetries, and draws parallels to string theory conjectures about operator lengths.

Contribution

It introduces and analyzes an action variable in the sine-Gordon model, linking it to Bäcklund transformations and hidden symmetries, providing a nonlinear analogue to free field solutions.

Findings

The action variable relates to Bäcklund transformations.

Hidden symmetry shifts breather phases.

Analogy to string theory operator length.

Abstract

It was conjectured that the classical bosonic string in AdS times a sphere has a special action variable which corresponds to the length of the operator on the field theory side. We discuss the analogous action variable in the sine-Gordon model. We explain the relation between this action variable and the Backlund transformations and show that the corresponding hidden symmetry acts on breathers by shifting their phase. It can be considered a nonlinear analogue of splitting the solution of the free field equations into the positive- and negative-frequency part.