Marginally Stable Topologically Non-Trivial Solitons in the Gross-Neveu Model

TL;DR

This paper demonstrates that in the large-N limit of the Gross-Neveu model, a kink and a trivial soliton form a marginally stable, bound state with no force between constituents, characterized by a modulus parameter.

Contribution

It reveals the existence of a marginally stable composite soliton formed by a kink and a trivial soliton in the Gross-Neveu model, with energy independent of their separation.

Findings

Kink and trivial soliton form a bound state at threshold.

The composite's energy is independent of soliton separation.

No force acts between the solitonic constituents in the large-N limit.

Abstract

We show that a kink and a topologically trivial soliton in the Gross-Neveu model form, in the large-N limit, a marginally stable static configuration, which is bound at threshold. The energy of the resulting composite system does not depend on the separation of its solitonic constituents, which serves as a modulus governing the profile of the compound soliton. Thus, in the large-N limit, a kink and a non-topological soliton exert no force on each other.