Quantum Gravity at the Turn of the Millennium

TL;DR

Horowitz surveys two leading quantum gravity programs—string theory and quantum geometry—and their main achievements and open problems. He highlights how string theory achieves perturbative finiteness, dualities, branes, and the AdS/CFT correspondence, alongside results on singularities and black hole radiation; quantum geometry yields a background-independent, nonperturbative quantization with spin networks, discrete area/volume spectra, and horizon-state counting that reproduces the Bekenstein-Hawking entropy $S_{bh} = \frac{A}{4 G \hbar}$ up to model-dependent factors. He notes that both routes feature holographic aspects and address topology change and unitarity, but differ in ontology: emergent spacetime in string theory versus fundamental quantum geometry. The paper concludes that the existence of a consistent quantum general relativity would likely favor the quantum geometry program, though a synthesis via holography and AdS/CFT remains a promising possibility.

Abstract

A very brief review is given of the current state of research in quantum gravity. Over the past fifteen years, two approaches have emerged as the most promising paths to a quantum theory of gravity: string theory and quantum geometry. I will discuss the main achievements and open problems of each of these approaches, and compare their strengths and weaknesses.