Jackiw–Teitelboim (JT) gravity has emerged as a powerful toy model for probing quantum aspects of black holes, holography, and spacetime dynamics near AdS₂ boundaries. Its simplicity allows for exact computations of gravitational path integrals, entanglement entropy, and thermodynamic properties while capturing essential features of more complex higher-dimensional theories. JT gravity also serves as the effective low-energy limit of the SYK model, providing a concrete framework for studying the AdS/CFT correspondence in two dimensions via quantum information approaches to quantum thermodynamics and quantum complexity. These connections make it an ideal laboratory for exploring quantum gravity, such as the origin of black hole entropy, the information paradox, and the role of boundary degrees of freedom.
The recent work A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product (arXiv:2410.10768) by G. Chirco, L. Vacchiano, and P. Vitale in the group presents a significant generalization of Jackiw–Teitelboim (JT) gravity by incorporating non-abelian gauge fields within the framework of a Poisson Sigma Model (PSM), derived from the dimensional reduction of a three-dimensional AdS₃ Chern-Simons theory based on the SO(2,2) algebra, with Wess-Zumino-Witten (WZW) boundary term. Embedding JT gravity within a larger symmetry framework opens avenues for exploring more complex holographic correspondences and understanding the role of additional degrees of freedom in low-dimensional gravity.
The case of a reduction from AdS₃ Chern-Simons leads to a PSM that naturally includes gravitational and non-abelian gauge fields. The boundary dynamics of the model are governed by coadjoint orbits of the Virasoro-Kac-Moody group, reflecting a symmetry structure of the semidirect product Diff(S¹) ⋉ 𝔤̂, where 𝔤̂ denotes the affine extension of a Lie algebra 𝔤. This structure generalizes the boundary Schwarzian action characteristic of JT gravity. The extended boundary action derived in this model corresponds to the low-energy effective action of certain Sachdev–Ye–Kitaev (SYK)-like tensor models. These models exhibit similar symmetry-breaking patterns, suggesting a deeper holographic relationship between higher-dimensional gravitational theories and lower-dimensional quantum systems. Further, including additional gauge fields leads to corrections in the computation of black hole entropy, which aligns with expectations from the dual SYK-like models.
This work offers a concrete realization of a gravitational dual to SYK-like models with internal symmetries, enriching the landscape of holographic dualities.
Further, the study of the duality of JT gravity with the low-energy effective action of Sachdev–Ye–Kitaev (SYK)-like tensor models bridges the research work in low-dimensional gravity with the forefront research on quantum thermalization and quantum complexity carried on within our division.
Current extensions of this work focus on generalizations of the PSM description of JT gravity via dissipative generalization of the Poisson geometry, to realize non-equilibrium or dissipative deformation of the JT/SYK duality. As a first attempt, the most recent work studies Jacobi and metriplectic extensions of Poisson Sigma Models, in place of the standard Lie–Poisson structure. In the SL(2, R) case, these deformations give rise to a dissipative extension of JT gravity, where gauge symmetry breaking in the bulk translates into modified asymptotic symmetries and a deformed Schwarzian theory on the boundary. These models encode irreversible dynamics, providing a mechanism for entropy production and offering a new framework to explore the thermodynamic behavior of black holes from first principles.
Dissipative extensions of JT gravity could yield novel insights into black hole thermodynamics by explicitly modeling entropy production and dissipation within a geometric framework. Interesting applications of this line include a non-equilibrium approach to holographic duality via generalized AdS₂/CFT₁ dualities that include time-asymmetric processes.
This framework again naturally relates to the work on quantum information in gravity, especially in the context of decoherence, scrambling, and open-system dynamics. Finally, on a more formal side, the topic involves the study of Leibniz (non-Lie) gauge algebroids, as natural structures underlying generalized gauge symmetries in the presence of dissipation.
These developments point toward a richer understanding of quantum gravity, where irreversible phenomena and entropic flows are encoded directly in the fundamental symmetry structure of spacetime.