The complete classification of stable static solitons in the gross-neveu model

We review our recent construction of all stable static fermion bags in the 1 + 1 dimensional Gross-Neveu model with N flavors of Dirac fermions, in the large N limit. In addition to the well known kink and topologically trivial solitons (which correspond, respectively, to the spinor and antisymmetric tensor representations of 0(2N)), there are also threshold bound states of a kink and a topologically trivial soliton: the heavier topological solitons (HTS). The mass of any of these newly discovered HTS’s is the sum of masses of its solitonic constituents, and it corresponds to the tensor product of their 0(2N) representations. Thus, it is marginally stable (at least in the large JV limit). Furthermore, its mass is independent of the distance between the centers of its constituents, which serves as a flat collective coordinate, or a modulus. There are no additional stable static solitons in the Gross-Neveu model. We have provided detailed derivation of the profiles, masses and fermion number contents of these static solitons elsewhere^1,2.