| Title |
The cyclic symmetries in the representations of unitary discrete subgroups / |
| Authors |
Jurčiukonis, Darius ; Lavoura, L |
| Full Text |
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| Is Part of |
8th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2022), 7-11 November, 2022, Baden-Baden, Germany.. Trieste : Sissa Medialab Srl. 2024, p. [1-5] |
| Abstract [eng] |
Dark matter may be stable because of a conserved ZN (cyclic) symmetry. Usually N is assumed to be 2, but it may also be larger than 2. This ZN is usually assumed to be in a direct product with some other symmetry group. The full symmetry group of the theory is then G = ZN ×G′. We suggest another possibility. Many discrete subgroups of U(D), for any D ≥ 2, have a non-trivial center ZN, even if they are not the direct product of that ZN with some other group. When that happens, the irreducible representations (‘irreps’) of the group may either represent all the elements of that ZN by the unit matrix, or else they may represent that ZN faithfully. If ordinary matter is placed in a representation where ZN is represented by 1, and dark matter is placed in irreps that represent ZN faithfully, then dark matter is stabilized by that ZN. We have scanned all the discrete groups in the SmallGroups library with order ≤ 2000 that are not the direct product of a cyclic group with some other group. We have determined their centers and whether they are subgroups of one or more groups SU(D) or U(D). We have found that very many groups, especially subgroups of U(D) but not of SU(D), have non-trivial centers ZN, mostly with N of the form 2p ×3q but also with other values of N. |
| Published |
Trieste : Sissa Medialab Srl |
| Type |
Conference paper |
| Language |
English |
| Publication date |
2024 |
| CC license |
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