Inverse scattering approach for massive Thirring models with integrable type-II defects

We discuss the integrability of the Bosonic and Grassmannian massive Thirring models in the presence of defects through the inverse scattering approach. We present a general method to compute the generating functions of modified conserved quantities for any integrable field equation associated to the m x m spectral linear problem. We apply the method to derive in particular the defect contributions for the number of occupation, energy and momentum of the massive Thirring models.

💡 Research Summary

The paper investigates the integrability of both the bosonic and Grassmannian massive Thirring models (MTM) when a type‑II defect is introduced, using the inverse scattering method (ISM). The authors begin by recalling that the MTM can be formulated through a Lax pair (U(λ), V(λ)) associated with an m × m linear spectral problem. For the bosonic case the fields are complex scalars ψ, ψ̄; for the Grassmannian case the fields are extended to include fermionic components, yielding a supersymmetric version of the model.

A type‑II defect is defined as a localized discontinuity at x = 0 that is not merely a jump condition but is governed by additional dynamical degrees of freedom (the “defect fields”). In the ISM framework the presence of the defect modifies the monodromy (or transfer) matrix T(λ) as follows: the full transfer matrix factorises into a product of three pieces, \