Number-Theory Dark Matter

TL;DR

This paper explores a novel number-theoretic approach to dark matter stability, proposing a discrete gauge symmetry derived from U(1)B-L and identifying conditions for anomaly cancellation and stable dark matter candidates.

Contribution

It introduces a new framework linking number theory, gauge symmetry, and dark matter stability, with specific constraints on fermion charges and a candidate particle.

Findings

Discrete Z_2(B-L) symmetry ensures dark matter stability.

Anomaly cancellation constrains fermion charge assignments.

A viable dark matter candidate is identified within the model.

Abstract

We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z_2(B-L). We introduce a set of chiral fermions charged under the U(1)B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z_2(B-L).