Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Product vacua with boundary states
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics