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

Autor(en)

Harald Grosse, Raimar Wulkenhaar

Abstrakt

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 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 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.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Münster

Journal

Journal of Geometry and Physics

Band

62

Seiten

1583-1599

Anzahl der Seiten

17

ISSN

0393-0440

DOI

https://doi.org/10.1016/j.geomphys.2012.03.005

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/4cdede21-a409-4923-8517-9d724642e1df