Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Symmetry allowed, but unobservable, phases in renormalizable Gauge Field
  Theory Models
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs