Superconnections and the Higgs Field

Abstract

Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection on a superbundle. We propose to take as superbundle the exterior algebra obtained from a Hermitian bundle with structure group U(n). Spontaneous symmetry breaking appears as a consequence of a non-vanishing scalar curvature. The U(1) Higgs model reformulates the Ginzburg-Landau theory, while the U(2) model relates to the electroweak theory with the relation $g^2=3g{4}^2$ for the gauge coupling constants, the formula ${\sin }^2\theta =1/4$ for the Weinberg angle, and the ratio $m_W^2:m_Z^2:m_H^2=3:4:12$ for the masses (squared) of the W, Z, and Higgs boson (at tree level).

21 pages, Latex, references added, minor change of content

References in corpus (1)

• The Einstein-Hilbert-Yang-Mills-Higgs Action and the Dirac-Yukawa Operator

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• All Order ${\alpha }^{\prime }$ Corrections to Fermionic Couplings of D-brane-Anti-D-brane Effective Actions
• On Special Limit of Non-Supersymmetric Effective Actions of type II String theory
• Quillen superconnections and connections on supermanifolds