Curvature corrections and Kac-Moody compatibility conditions

TL;DR

This paper investigates the restrictions on curvature corrections in gravitational theories imposed by their associated Kac-Moody algebra structures, particularly focusing on E10 and its implications for M-theory quantum corrections.

Contribution

It demonstrates that leading quantum corrections in M-theory align with fundamental weights of E10 and explores the generalization of this relationship to other over-extended algebras.

Findings

Quantum corrections of M-theory relate to E10 fundamental weights.

Compatibility conditions for curvature corrections depend on algebraic weight structures.

Comparison with known quantum corrections supports the algebraic approach.

Abstract

We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac--Moody algebras, following the initial work on E10 in Class. Quant. Grav. 22 (2005) 2849. We first emphasize that the leading quantum corrections of M-theory can be naturally interpreted in terms of (non-gravity) fundamental weights of E10. We then heuristically explore the extent to which this remark can be generalized to all over-extended algebras by determining which curvature corrections are compatible with their weight structure, and by comparing these curvature terms with known results on the quantum corrections for the corresponding gravitational theories.