Progress and problems in quantum gravity

TL;DR

This paper reviews the challenges in quantum gravity, discusses recent reformulation attempts, and highlights how 2D dilaton quantum gravity offers a background-independent approach with significant theoretical insights.

Contribution

It demonstrates that 2D dilaton quantum gravity can achieve a background-independent quantum theory, providing solutions to longstanding problems and advancing superstring theory research.

Findings

Introduction of Poisson-Sigma models

Verification of the virtual Black Hole concept

Extensions to N=(1,1) and N=(2,2) supergravity

Abstract

From the point of view of an uncompromising field theorist quantum gravity is beset with serious technical and, above all, conceptual problems with regard especially to the meaning of genuine "physical" observables. This situation is not really improved by the appearance of recent attempts to reformulate gravity within some novel framework.However, the original aim, a background-independent quantum theory of gravity, can be achieved in a particular area, namely 2d dilaton quantum gravity without any assumptions beyond standard quantum field theory. Some important by-products of the research of the "Vienna School" include the introduction of the concept of Poisson-Sigma models, a verification of the "virtual Black Hole" and the extensions to N = (1,1) and N = (2,2) 2d-supergravity, for which complete solutions of some old problems have been possible which are relevant for superstring theory