Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-trivial flat connections on the 3-torus I: G_2 and the orthogonal
  groups   We propose a construction of non-trivial vacua for Yang-Mills theories on the
3-torus. Although we consider theories with periodic boundary conditions,
twisted boundary conditions play an essential auxiliary role in our
construction. In this article we will limit ourselves to the simplest case,
based on twist in SU(2) subgroups. These reproduce the recently constructed new
vacua for SO(N) and G_2 theories on the 3-torus. We show how to embed the
results in the other exceptional groups F_4 and E_{6,7,8} and how to compute
the relevant unbroken subgroups. In a subsequent article we will generalise to
SU(N > 2) subgroups. The number of vacua found this way exactly matches the
number predicted by the calculation of the Witten index in the infinite volume.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int