  We consider pseudo Nambu-Goldstone bosons arising from Dirac fermions
transforming in real representations of a confining gauge group as dark matter
candidates. We consider a special case of two Dirac fermions and couple the
resulting dark sector to the Standard Model using a vector mediator. Within
this construction, we develop a consistent low energy effective theory, with
special attention to Wess-Zumino-Witten term given the topologically
non-trivial coset space. We furthermore include the heavier spin-0 flavour
singlet state and the spin-1 vector meson multiplet, by using the Hidden Local
Symmetry Lagrangian for the latter. Although we concentrate on special case of
two flavours, our results are generic and can be applied to a wider variety of
theories featuring real representations. We apply our formalism and comment on
the effect of the flavour singlet for dark matter phenomenology. Finally, we
also comment on generalisation of our formalism for higher representations and
provide potential consequences of discrete symmetry breaking.
