Abstract
We investigate structural aspects of JT gravity through its BF description. In particular, we provide evidence that JT gravity should be thought of as (a coset of) the noncompact subsemigroup SL+(2, ℝ) BF theory. We highlight physical implications, including the famous Plancherel measure sinh 2π sqrt{E} . Exploiting this perspective, we investigate JT gravity on more generic manifolds with emphasis on the edge degrees of freedom on entangling surfaces and factorization. It is found that the one-sided JT gravity degrees of freedom are described not just by a Schwarzian on the asymptotic boundary, but also include frozen SL+(2, ℝ) degrees of freedom on the horizon, identifiable as JT gravity black hole states. Configurations with two asymptotic boundaries are linked to 2d Liouville CFT on the torus surface.
Highlights
When considering models of two-dimensional gravity, the Jackiw-Teitelboim (JT) theory plays a privileged role [1, 2]: 1 S[g, Φ] = 16πG2d2x√−g Φ R(2) − Λ + SGH. (1.1)It consists of a 2d metric gμν, whose only physical degree of freedom is the Ricci scalar R, and a dilaton field Φ
This model is the spherical dimensional reduction of pure 3d gravity with cosmological constant Λ and as such, it is the closest one can get in two dimensions to a dynamical pure quantum gravity theory
Though the emphasis in this work is not on such correlation functions, at several instances we will write down some amplitudes, with the goal of showing that the BF perspective on JT allows us to understand dynamics of JT quantum gravity on generic manifolds
Summary
When considering models of two-dimensional gravity, the Jackiw-Teitelboim (JT) theory plays a privileged role [1, 2]:. It consists of a 2d metric gμν, whose only physical degree of freedom is the Ricci scalar R, and a dilaton field Φ This model is the spherical dimensional reduction of pure 3d gravity with cosmological constant Λ and as such, it is the closest one can get in two dimensions to a dynamical pure quantum gravity theory.. This raises issues regarding a Hilbert space interpretation of such quantum systems [27, 51], which are intrinsic to JT To address this and other aspects of the factorization problem of [51], one would have to consider a specific UV-ancestor of JT, like SYK, and find a discretized set of microstates. Generic correlation functions with Wilson lines inserted, possibly crossed, can be written down using a diagrammatic construction. Though the emphasis in this work is not on such correlation functions, at several instances we will write down some amplitudes, with the goal of showing that the BF perspective on JT allows us to understand dynamics of JT quantum gravity on generic manifolds
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
