Duality between Dirac fermions in curved spacetime and optical solitons in non-linear Schrodinger model: magic of $$1+1$$ 1+1 -dimensional bosonization

Abstract

Abstract Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized Sine–Gordon model, both living in $$1+1$$ 1+1 -dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.