Stringy algebras, stretched horizons, and quantum-connected wormholes

While the supergravity limit of AdS/CFT has been extensively explored, the regime in which stringy dynamics dominate, characterized by the emergence of an infinite tower of higher-spin massive modes, is far less understood. In this work, we leverage techniques from algebraic quantum field theory to investigate the extent to which hallmark features of bulk gravity survive at finite string tension and the emergence of intrinsically stringy phenomena. Working in the $g_s\rightarrow 0$ limit, we model excited string modes as free particles and demonstrate that the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other. We propose that this leads to a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces. When stretched horizons exist, there is an associated nontrivial horizon $\star$-algebra.Furthermore, applying the algebraic ER=EPR proposal leads to the emergence of type III${}_{0}$ von Neumann factors, which provide an intriguing characterization of how such regions can have a quantum Einstein-Rosen bridge even if they are geometrically disjoint.