Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge invariance for the massive axion   A massive gauge invariant formulation for scalar ($\phi$) and antisymmetric
($C_{mnp}$) fields with a topological coupling, which provides a mass for the
axion field, is considered. The dual and local equivalence with the non-gauge
invariant proposal is established, but on manifolds with non-trivial
topological structure both formulations are not globally equivalent.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph