Speaker
Description
Dark matter may be stable because of a conserved Z_p (cyclic) symmetry. Usually p is assumed to be 2, but it may also be larger than 2.
This Z_p is usually assumed to be in a direct product with some other symmetry group. The full symmetry group of the theory is then G = Z_p x G'. We suggest another possibility.
Many discrete subgroups of U(n), for any n > 2, have a non-trivial center Z_p, even if they are not the direct product of that Z_p with some other group. When that happens, the irreducible representations (irreps) of the group may either represent all the elements of that Z_p by the unit matrix, or else they may represent that Z_p faithfully. If ordinary matter is placed in a representation where Z_p is represented by 1, and dark matter is placed in irreps that represent Z_p faithfully, then dark matter is stabilized by that Z_p.
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(n) or U(n). We have found that very many groups, especially subgroups of U(n) but not of SU(n), have non-trivial centers Z_p, mostly with p of the form 2^a times 3^b but also with other values of p.
