Astrophysical observations provide strong evidence that more than 80% of all matter in the Universe is in the form of dark matter (DM). Two leading candidates of particles beyond the Standard Model that could constitute all or a fraction of the DM content are the so-called Weakly Interacting Massive Particles (WIMPs) and Axion-Like Particles (ALPs). The upcoming Cherenkov Telescope Array, which will observe gamma rays between 20 GeV and 300 TeV with unprecedented sensitivity, will have unique capabilities to search for these DM candidates. A particularly promising target for WIMP searches is the Galactic Center. WIMPs with annihilation cross sections correctly producing the DM relic density will be detectable with CTA, assuming an Einasto-like density profile and WIMP masses between 200 GeV and 10 TeV. Regarding new physics beyond DM, CTA observations will also enable tests of fundamental symmetries of nature such as Lorentz invariance.
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