From effective strings to the simplest theory of quantum gravity

We revisit the effective theory of long relativistic strings, such as confining flux tubes in QCD.
Motivated by the recent lattice data we resolve an interesting controversy regarding the so-called Polchinski--Strominger interaction. Then we reconsider  the worldsheet theory of an infinitely long critical string.Contrary to naive expectations, this theory is non-trivial and provides the simplest example of an integrable theory of quantum gravity. We illustrate this by constructing its exact factorizable $S$-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables,  a minimal length, a maximum achievable (Hagedorn) temperature, as well as (integrable relatives of) black holes. We argue that considered as a UV complete relativistic 2-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, ``asymptotic fragility".