The decay of unstable strings in SU(2) Yang-Mills theory

We investigate the stability of strings connecting charges Q in the representation {2Q+1} of SU(2) Yang-Mills theory in (2+1) dimensions. While the fundamental {2}-string between two charges Q=1/2 is unbreakable and stable, the string connecting static charges transforming under any other representation Q>1/2 is unstable and decays. A charge Q=1 can be completely screened by gluons and so the adjoint {3}-string ultimately breaks. A charge Q=3/2 can be only partially screened to a fundamental charge Q=1/2. Thus, stretching a {4}-string beyond a critical length, it decays into the stable {2}-string by gluon pair creation. The complete breaking of a {5}-string happens in two steps, it first decays into a {3}-string and then breaks completely. A phenomenological constituent gluon model provides a good quantitative description of the energy of the screened charges at the ends of an unstable string.

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