Algebra and Geometry from Chords

In double-scaled SYK, the chord diagrams of Berkooz et al. give rise to a bulk algebra and geometry. The algebra is a "quantum deformation" of the JT gravitational algebra that includes a deformation of SL(2,R). The growth of operator size (in particular, its finite temperature, sub-maximal Lyapunov behavior) is governed by this algebra. The deformed SL(2,R) acts in a somewhat unusual manner on the bulk geometry.