Solving the Simplest Theory of Quantum Gravity

TL;DR

This paper solves a simple quantum gravity model using an exact S-matrix, revealing key features like a minimal length, maximum temperature, and black hole analogs, and introduces a new RG flow behavior called 'asymptotic fragility.'

Contribution

It provides an exact solution to a basic quantum gravity model and uncovers novel properties such as asymptotic fragility in its RG flow.

Findings

Exact factorizable S-matrix constructed

Finite volume spectrum derived analytically

Identification of 'asymptotic fragility' RG behavior

Abstract

We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. 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. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic two-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, "asymptotic fragility". Asymptotically fragile flows do not originate from a UV fixed point.