A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations

We interpret reported hints of a Standard Model Higgs boson at ~ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10^6 and 10^18 GeV. Such a small value of lambda can be understood in terms of models with high-scale SUSY breaking if the Kahler potential possesses a shift symmetry, i.e., if it depends on H_u and H_d only in the combination (H_u+\bar{H}_d). This symmetry is known to arise rather naturally in certain heterotic compactifications. We suggest that such a structure of the Higgs Kahler potential is common in a wider class of string constructions, including intersecting D7- and D6-brane models and their extensions to F-theory or M-theory. The latest LHC data may thus be interpreted as hinting to a particular class of compactifications which possess this shift symmetry.