Technicolor with a 125 GeV Higgs Boson

Bosonic technicolor models accommodate fermion masses via a Higgs doublet that acquires a vacuum expectation value when technifermions condense. We point out that these models are severely constrained by vacuum stability if the Higgs boson mass is near 125 GeV, the value suggested by LHC data. The Higgs quartic coupling in bosonic technicolor is typically smaller at the weak scale than in the Standard Model, while the top quark Yukawa coupling is larger. We find that the running quartic coupling remains positive below a reasonably defined cut off only in a narrow region of the model's parameter space. This region is only slightly enlarged if one allows a metastable vacuum with a lifetime longer than the age of the universe.