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We generalise previous studies on the extension of Goldstone's theorem fromHermitian to non-Hermitian quantum field theories with Abelian symmetries totheories possessing a glocal non-Abelian symmetry. We present a detailedanalysis for a non-Hermitian field theory with two complex two component scalarfields possessing a SU(2)-symmetry and indicate how our finding extend to thegeneral case. In the PT-symmetric regime and at the standard exceptional pointthe Goldstone theorem is shown to apply, although different identificationprocedures need to be employed. At the zero exceptional points the Goldstoneboson can not be identified. Comparing our approach, based on thepseudo-Hermiticity of the model, to an alternative approach that utilisessurface terms to achieve compatibility for the non-Hermitian system, we findthat the explicit forms of the Goldstone boson fields are different.

Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories