We couple non-linear σ-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross-Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.
Abdalla, E., & Abdalla, M. C. B. (1996). Gravitational interactions of integrable models. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 365(1–4), 41–45. https://doi.org/10.1016/0370-2693(95)01301-6