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Higgs mass, superconnections, and the TeV-scale left-right symmetric model

We discuss the physical implications of formulating the Standard Model (SM) in terms of the superconnection formalism involving the superalgebra s u ( 2 / 1 ) . In particular, we discuss the prediction of the Higgs mass according to the formalism and point out that it is ∼ 170 GeV , in clear disagreement with experiment. To remedy this problem, we extend the formalism to the superalgebra s u ( 2 / 2 ) , which extends the SM to the left-right symmetric model (LRSM) and accommodates a ∼ 126 GeV Higgs boson. Both the SM in the s u ( 2 / 1 ) case and the LRSM in the s u ( 2 / 2 ) case are argued to emerge at ∼ 4 TeV from an underlying theory in which the spacetime geometry is modified by the addition of a discrete extra dimension. The formulation of the exterior derivative in this model space suggests a deep connection between the modified geometry, which can be described in the language of noncommutative geometry, and the spontaneous breaking of the gauge symmetries. The implication is that spontaneous symmetry breaking could actually be geometric/quantum gravitational in nature. The nondecoupling phenomenon seen in the Higgs sector can then be reinterpreted in a new light as due to the mixing of low energy (SM) physics and high energy physics associated with quantum gravity, such as string theory. The phenomenology of a TeV scale LRSM is also discussed, and we argue that some exciting discoveries may await us at the LHC, and other near-future experiments.