  In the absence of a clear hint of dark matter (DM) signals in the GeV regime
so far, heavy, $\mathcal{O}$(TeV) DM candidates are gradually earning more and
more attention within the community. Among others, extra-dimensional
\textit{brane-world} models may produce thermal DM candidates with masses up to
100 TeV. These heavy DM candidates could be detected with the next generation
of very-high-energy gamma-ray observatories such as the Cherenkov Telescope
Array (CTA). In this work, we study the sensitivity of CTA to branon DM via the
observation of representative astrophysical DM targets, namely dwarf spheroidal
galaxies. In particular, we focus on Draco and Sculptor, two well-known dwarfs
visible from the Northern and Southern Hemisphere, respectively. For each of
these targets, we simulated 300\,h of CTA observations and studied the
sensitivity of both CTA-North and CTA-South to branon annihilations using the
latest publicly available instrument response functions and most recent
analysis tools. We computed annihilation cross section values needed to reach a
$5\sigma$ detection as a function of the branon mass. Additionally, in the
absence of a predicted DM signal, we obtained $2\sigma$ upper limits on the
annihilation cross section. These limits lie $1.5-2$ orders of magnitude above
the thermal relic cross section value, depending on the considered branon mass.
Yet, CTA will allow to exclude a significant portion of the brane tension-mass
parameter space in the $0.1-60$ TeV branon mass range, and up to tensions of
$\sim 10$ TeV. More importantly, CTA will significantly enlarge the region
already excluded by AMS and CMS, and will provide valuable complementary
information to future SKA radio observations. We conclude that CTA will possess
potential to constrain brane-world models and, more in general, TeV DM
candidates.
