  We explore whether the axion which solves the strong CP problem can naturally
be much lighter than the canonical QCD axion. The $Z_\mathcal{N}$ symmetry
proposed by Hook, with $\mathcal{N}$ mirror and degenerate worlds coexisting in
Nature and linked by the axion field, is considered in terms of generic
effective axion couplings. We show that the total potential is safely
approximated by a single cosine in the large $\mathcal{N}$ limit, and we
determine the analytical formula for the exponentially suppressed axion mass.
The resulting universal enhancement of all axion interactions relative to those
of the canonical QCD axion has a strong impact on the prospects of axion-like
particle experiments such as ALPS II, IAXO and many others. The finite density
axion potential is also analyzed and we show that the $Z_\mathcal{N}$
asymmetric background of high-density stellar environments sets already
significant model-independent constraints: $3\le\mathcal{N}\lesssim47$ for an
axion scale $f_a\lesssim 2.4\times10^{15}$ GeV, with tantalizing discovery
prospects for any value of $f_a$ and down to $\mathcal{N}\sim9$ with future
neutron star and gravitational wave data, down to the ultra-light mass region.
In addition, two specific ultraviolet $Z_\mathcal{N}$ completions are
developed: a composite axion one and a KSVZ-like model with improved
Peccei-Quinn quality.
