Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Softly-broken $A_4$ or $S_4$ 3HDMs with stable states   We study multi-Higgs models with a triplet of $A_4$ or $S_4$ symmetry that is
softly-broken. Focusing on parameters that softly break the respective
symmetries but preserve the directions of the vacuum expectation values of the
triplet we analyse the masses of physical states and discuss their decays. In
contrast with previously studied symmetries, we find some cases with stable
states that are protected by residual symmetries left unbroken by both the
soft-breaking parameters and by the vacuum.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs