Gravitational Interactions of integrable models

TL;DR

This paper demonstrates that integrability properties of symmetric space models and Gross--Neveu-type models are preserved when coupled to Liouville gravity, extending the understanding of integrable systems in gravitational contexts.

Contribution

It shows that integrability of certain matter models remains intact when coupled to Liouville gravity, including both bosonic and fermionic models.

Findings

Integrability of symmetric space models is preserved under coupling to Liouville gravity.

Gross--Neveu-type models also retain integrability properties in this gravitational setting.

The results support the universality of integrability in coupled matter-gravity systems.

Abstract

We couple non-linear $\sigma$-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.