A closed clockwork theory: \(\mathbb{Z}_2\) parity and more

• Published in: arXiv.org 2022-11
• Main Authors: Choudhury, Debajyoti, Maharana, Suvam
• Format: Article
• Language: English
• Subjects: Boundary conditions; Clockwork; Couplings; Dark matter; Dilatons; Parity; Symmetry; Topology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2207.07226

We develop a new class of clockwork theories with an augmented structure of the near-neighbour interactions along a one-dimensional closed chain. Such a topology leads to new and attractive features in addition to generating light states with hierarchical couplings via the usual clockwork mechanism. For one, there emerges a \(\mathbb{Z}_2\) symmetry under the exchange of fields resulting in a physical spectrum consisting of states, respectively even and odd under the exchange parity with a two-fold degeneracy at each level. The lightest odd particle, being absolutely stable, could be envisaged as a potential dark matter candidate. The theory can also be obtained as a deconstruction of a five-dimensional theory embedded in a geometry generated by a linear dilaton theory on a \(S^1/\mathbb{Z}_2\) orbifold with three equidistant 3-branes. Analogous to the discrete picture, the \(\mathbb{Z}_2\) symmetry in the bulk theory necessitates the existence of a KK spectrum of even and odd states, with doubly degenerate modes at each KK level when subject to certain boundary conditions.