A Note on the Symmetries and Renormalisability of (Quantum) Gravity

TL;DR

This paper discusses the role of symmetries, K-theory, and noncommutative geometry in quantum gravity, and explores the implications of Connes and Kreimer's work on renormalization and the Riemann-Hilbert correspondence.

Contribution

It highlights the importance of advanced mathematical frameworks like K-theory and noncommutative geometry in understanding quantum gravity and comments on recent renormalization approaches.

Findings

Symmetries in gravity may involve K-theory and noncommutative geometry.

Connections between renormalization, Riemann-Hilbert, and quantum gravity are discussed.

Open questions raised about the mathematical structures in quantum gravity.

Abstract

We make some remarks on the group of symmetries in gravity; we believe that K-theory and noncommutative geometry inescepably have to play an important role. Furthermore we make some comments and questions on the recent work of Connes and Kreimer on renormalisation, the Riemann-Hilbert correspondence and their relevance to quantum gravity.