Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dihedral symmetry in $SU(N)$ Yang-Mills theory   We point out that charge conjugation and coordinate reflection symmetries do
not commute with the center symmetry of $SU(N)$ YM theory when $N>2$. As a
result, for generic values of the $\theta$ angle, the group of discrete
zero-form symmetries of YM theory on e.g. the spacetime manifold
$\mathbb{R}^3\times S^1$ includes the dihedral group $D_{2N}$ which is
non-Abelian for $N>2$. At $\theta = \pi$, the non-Abelian factor in the
symmetry group is enhanced to $D_{4N}$ due to discrete 't Hooft anomaly
considerations. We illustrate these results in YM theory as well as in a simple
quantum mechanical model, where we study representation theory as a function of
$\theta$ angle.

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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin