On the Worldsheet Formulation of the Six-Dimensional Self-Dual String

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Despite recent evidence indicating the existence of a new kind of self-dual six-dimensional superstring, no satisfactory worldsheet formulation of such a string has been proposed. In this note we point out that a theory built from Z₄ parafermions may have the right properties to describe the light-cone conformal field theory of this string. This indicates a possible worldsheet formulation of this theory.