Strings, loops and others: a critical survey of the present approaches to quantum gravity

TL;DR

This paper critically reviews various theoretical approaches to quantum gravity, highlighting their achievements, challenges, and recent advances in understanding quantum spacetime and black hole entropy.

Contribution

It provides a comprehensive comparison of current quantum gravity theories and discusses recent progress and difficulties in the field.

Findings

String theory and loop quantum gravity have made significant progress.

Challenges remain in unifying different approaches and understanding black hole entropy.

Recent advances have improved our understanding of quantum spacetime properties.

Abstract

I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity (Regge calculus, dynamical triangulations and simplicial models), Euclidean quantum gravity, perturbative quantum gravity, quantum field theory on curved spacetime, noncommutative geometry, null surfaces, topological quantum field theories and spin foam models. I also briefly review several recent advances in understanding black hole entropy and attempt a critical discussion of our present understanding of quantum spacetime.