Global (Poisson-)Lie Symmetries and 2D Dilaton GravityConfirmed

by Christopher Pollack (Perimeter Institute for Theoretical Physics)

Monday May 11, 2026, 2:00 PM → 2:30 PM America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

It is well known that quantum group structures play an important role in the quantization of low-dimensional, 2D and 3D, gravity. The classical origin of these structures has recently been clarified through the identification of Poisson-Lie symmetries; a type of symmetry which genuinely extends the standard Noether notion of symmetry in several ways. This talk begins by reviewing our formulation of Poisson-Lie symmetries within the covariant phase space formalism, highlighting how they generalize conventional Noether symmetry notions. We then turn to studying two-dimensional dilaton gravity, a class of solvable models capturing key features of quantum gravity and near-horizon physics, including the Jackiw–Teitelboim (JT) model. These theories are typically organized by a (potentially non-linear) sl(2,R) Noether gauge symmetry, whose Casimir labels the mass of spacetime solutions. The first main result of this talk shows that demanding a consistent notion of gauge charge “addition” in such models leads to the appearance of an additional global symmetry, not of the Noether type but instead of the Poisson-Lie type. This requirement severely constrains the large class of 2D dilaton gravity models, selecting only three compatible classes of dilaton potentials: zero, linear (JT/dS/AdS), and sinh-type (Liouville gravity). The second main result of this talk concerns the physical implications of these new, non-Noetherian, global Poisson-Lie symmetries. Focusing on the linear (JT) case for this talk, we show that the Poisson-Lie symmetry acts non-trivially on solutions, allowing continuous and arbitrary shifts of the spacetime mass while leaving the local geometry unchanged. We also derive the associated Ward identity in the quantum theory and discuss. This work is ongoing, so feedback and new perspectives on these surprising results is very welcome!