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Observing that the Hamiltonian of the renormalisable scalar field theory on4-dimensional Moyal space A is the square of a Dirac operator D of spectraldimension 8, we complete (A,D) to a compact 8-dimensional spectral triple. Weadd another Connes-Lott copy and compute the spectral action of thecorresponding U(1)-Yang-Mills-Higgs model. We find that in the Higgs potentialthe square \phi^2 of the Higgs field is shifted to \phi * \phi + const X_\mu *X^\mu, where X_\mu is the covariant coordinate. The classical field equationsof our model imply that the vacuum is no longer given by a constant Higgsfield, but both the Higgs and gauge fields receive non-constant vacuumexpectation values.

8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory