A search for high-energy neutrinos coming from the direction of the Galactic Centre is performed using the data recorded by the ANTARES neutrino telescope from 2007 to 2012. The event selection criteria are chosen to maximise the sensitivity to possible signals produced by the self-annihilation of weakly interacting massive particles accumulated around the centre of the Milky Way with respect to the atmospheric background. After data unblinding, the number of neutrinos observed in the line of sight of the Galactic Centre is found to be compatible with background expectations. The 90% C.L. upper limits in terms of the neutrino+anti-neutrino flux, Φνμ+ν¯μ, and the velocity averaged annihilation cross-section, 〈σAv〉, are derived for the WIMP self-annihilation channels into bb¯, W+W-, τ+τ-, μ+μ-, νν¯. The ANTARES limits for 〈σAv〉 are shown to be the most stringent for a neutrino telescope over the WIMP masses 25 GeV < MWIMP < 10 TeV.
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