Fermionic sectors for the Kodama state
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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.
4 pages
4 pages