Hidden Symmetries and Dirac Fermions

TL;DR

This paper explores how Dirac fermions can be integrated into hidden duality symmetries in gravitational theories, showing their compatibility with both finite and overextended symmetries and analyzing their impact on chaotic behavior.

Contribution

It demonstrates the compatibility of Dirac fermions with duality symmetries and extends the understanding of their role in the symmetry structure of gravitational theories.

Findings

Dirac fermions can be incorporated into duality symmetries via Pauli couplings.

Compatibility with overextended symmetry G++ is established.

Dirac fields influence the chaotic BKL behavior, removing chaos.

Abstract

In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show that the Pauli couplings to the p-forms can be adjusted, for all simple (split) groups, so that the fermions transform in a representation of the maximal compact subgroup of the duality group G in three dimensions. Second, we investigate how the Dirac fermions fit in the conjectured hidden overextended symmetry G++. We show compatibility with this symmetry up to the same level as in the pure bosonic case. We also investigate the BKL behaviour of the Einstein-Dirac-p-form systems and provide a group theoretical interpretation of the Belinskii-Khalatnikov result that the Dirac field removes chaos.