Generalize the discretization to nonlinear dilaton gravities

Determine to what extent the homogeneous Regge and split triangulation/dual-complex discretization developed for linear dilaton gravity can be generalized to nonlinear two-dimensional dilaton gravities described by Poisson sigma models, and whether the split triangulation/dual-complex structure survives in an appropriate form.

Background

The paper treats the simplest linear dilaton-gravity model, whose gauge-theoretic formulation is an ordinary BF theory. More general models, including Liouville-type gravity, are described by nonlinear Poisson sigma models instead.

The authors point out that the algebraic structure would then be deformed and explicitly leave unresolved both the extent of a possible generalization and the survival of the split triangulation/dual-complex description.

References

We have also restricted our attention to the simplest dilaton-gravity model. More general two-dimensional dilaton gravities are naturally described by non-linear Poisson sigma models , rather than by an ordinary BF theory, and include models such as Liouville-type gravity. In such cases, one expects the underlying algebraic structure to be correspondingly deformed, potentially involving further quantum-group-like structures. It would be interesting to determine to what extent the present discretization can be generalized to these non-linear theories and whether the split triangulation/dual-complex picture survives in an appropriate form.

— Regge Dilaton Gravity from BF Theory  (2610.21058 - Girelli et al., 15 Oct 2026) in Conclusion