Non-topological soliton

In quantum field theory, a non-topological soliton (NTS) is a field configuration possessing, contrary to a topological one, a conserved Noether charge and stable against transformation into usual particles of this field for the following reason. For fixed charge Q, the mass sum of Q free particles exceeds the energy (mass) of the NTS so that the latter is energetically favorable to exist.

The interior region of an NTS is occupied by vacuum different from the ambient vacuum. The vacuums are separated by the surface of the NTS representing a domain wall configuration (topological defect), which also appears in field theories with broken discrete symmetry. Infinite domain walls contradict cosmology, but the surface of an NTS is closed and finite, so its existence would not be contradictory. If the topological domain wall is closed, it shrinks because of wall tension; however, due to the structure of the NTS surface, it does not shrink since the decrease of the NTS volume would increase its energy.

Quantum field theory has been developed to describe the elementary particles. However, in the mid 1970s it was found out that this theory predicts one more class of stable compact objects: non-topological solitons. The NTS represents an unusual coherent state of matter, called also bulk matter. Models were suggested for the NTS to exist in forms of stars, quasars, the dark matter and nuclear matter.

An NTS configuration is the lowest energy solution of classical equations of motion possessing a spherical symmetry. Such a solution has been found for a rich variety of field Lagrangians. One can associate the conserved charge with global, local, Abelian and non-Abelian symmetry. It appears to be possible the NTS configuration with bosons as well as with fermions to exist. In different models either one and the same field carries the charge and binds the NTS, or there are two different fields: charge carrier and binding field.

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