8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
arXiv:0709.0095 · doi:10.1016/j.geomphys.2012.03.005
Abstract
Observing that the Hamiltonian of the renormalisable scalar field theory on 4-dimensional Moyal space A is the square of a Dirac operator D of spectral dimension 8, we complete (A,D) to a compact 8-dimensional spectral triple. We add another Connes-Lott copy and compute the spectral action of the corresponding U(1)-Yang-Mills-Higgs model. We find that in the Higgs potential the square Ï^2 of the Higgs field is shifted to Ï* Ï+ const X_μ* X^μ, where X_μis the covariant coordinate. The classical field equations of our model imply that the vacuum is no longer given by a constant Higgs field, but both the Higgs and gauge fields receive non-constant vacuum expectation values.
LaTeX, 23 pages. Preface added which explains the mathematical achievements since v1; these are presented in arXiv:1108.2184. Incorrect section about field equations removed