SL(2,R) Symmetry in the JT/SYK Correspondence

The AdS/CFT correspondence is a duality that has had a profound impact on theoretical physics over the last decades. This project is concerned with the study of a pair of theories that fall under a similar classification, namely (Nearly-AdS₂/Nearly-CFT₁). The bulk theory is a 2d dilaton gravity called JT gravity, where the spacetime is asymptotically described by AdS₂, and wherein an interaction between the two boundaries is considered. The gravitational modes correspond to the boundary dynamics, governed by a Schwarzian action. This theory bears the interpretation of an eternal wormhole which is rendered traversable by the topological-censorship-evading non-local interaction of the boundaries. The boundary theory is described by two coupled SYK models. Both theories have the same low-energy effective description, which allows for the interpretation of SYK observables as those of a gravitational sector. In the low-but-not-too low energy limit, the system exhibits modes whose spectrum is governed by a SL(2,R) symmetry, which has interpretations in both SYK and JT theory. This symmetry is analyzed and examined from the SYK prespective.