Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory

We investigate the Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism for non-Hermitian field theories with local non-Abelian gauge symmetry in different regions of their parameter spaces. We demonstrate that the two aspects of the mechanism, that is giving mass to gauge vector bosons and at the same time preventing the existence of massless Goldstone bosons, remain to be synchronized in all regimes characterized by a modified CPT symmetry. In the domain of parameter space where the "would be Goldstone bosons" can be identified the gauge vector bosons become massive and the Goldstone bosons cease to exist. The mechanism is also in tact at the standard exceptional points. However, at the zero exceptional points, that is when the eigenvalues of the mass squared matrix vanish irrespective of the symmetry breaking, the mechanism breaks down as the Goldstone bosons can not be identified and the gauge vector bosons remain massless. This breakdown coincides with the vanishing of the CPT inner product of symmetry breaking vacua defined on the eigenvector space of mass squared matrix. We verify this behaviour for a theory with SU(N) symmetry in which the complex scalar fields are taken in the fundamental as well as in the adjoint representation.