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

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Grosse, Harald²  Wulkenhaar, Raimar¹ 

[1] Univ Munster, Math Inst, D-48149 Munster, Germany

[2] Univ Wien, Inst Theoret Phys, A-1090 Vienna, Austria

关键词: Noncommutative differential geometry;    Spectral action;    Yang-Mills and other gauge theories;   

DOI  :  10.1016/j.geomphys.2012.03.005

来源: Elsevier

【 摘 要 】

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. (C) 2012 Published by Elsevier B.V.

【 授权许可】

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