Accidental Symmetries, Hilbert Series, and Friends

Abstract: Accidental symmetries are ubiquitous in EFTs and have important phenomenological consequences. They can be verified by computing and comparing the Hilbert series. To demonstrate the technology, I show three classes of accidental symmetries that hold to all orders for non-derivative interactions. These are generalizations of the custodial symmetry in the Higgs sector of the Standard Model. More systematic approach can be achieved by introducing a novel mathematical construct — a "friendship" relation between subgroups. With this, we derive new criteria for verifying and identifying accidental symmetries more efficiently without computing the Hilbert series.