Fermionic sectors for the Kodama state

TL;DR

This paper explores how the quantum state space of gravity, unlike nonabelian Yang-Mills theories, can have higher-dimensional representations, including spin 1/2 sectors, especially for topologies with positive scalar curvature.

Contribution

It demonstrates the existence of fermionic (spin 1/2) sectors in the quantum state space of gravity, providing a potential resolution to recent criticisms.

Findings

Kodama state admits 2D spin 1/2 representations

Higher-dimensional sectors exist for topologies with positive scalar curvature

Addresses recent criticisms regarding the quantum state space of gravity

Abstract

Diffeomorphisms not connected to the identity can act nontrivially on the quantum state space for gravity. However, in stark contrast to the case of nonabelian Yang-Mills field theories, for which the quantum state space is always in 1 dimensional representation of the large gauge transformations, the quantum state space for gravity can have higher dimensional representations. In particular, the Kodama state will have 2 dimensional representations, that is sectors with spin 1/2, for many topologies that admit positive scalar curvature. The existence of these spin 1/2 states are used to point out a possible answer to certain criticisms raised recently in the literature.