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I have seen the statement that the Standard Model has a Landau pole, or at least it its believed that it does at $\sim 10^{34}$ GeV. Has this actually been proven (at least in perturbation theory, as in QED) or what kind of evidence is there to support this?

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I'm not sure if it's the case, and it's possible that the answer is sensitive to measured constants (the Higgs mass, the top mass, alpha-strong). A well-known recent paper that runs relevant SM couplings up to the Planck scale is - it hints that the Higgs coupling doesn't blow up but actually almost vanishes at the Planck scale. – Vibert Feb 19 '13 at 15:29
@Vibert: The $\lambda$ result in that paper is interesting, but the $U(1)$ coupling shows no signs of slowing down. I think right now I'd bet that the Standard Model has at least one Landau pole. – user1504 Feb 20 '13 at 13:16

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I am not sure whether the standard model has a Landau pole at $10^{34}$ GeV but there are two obstacles to providing a definite answer to the question: (1) perturbation theory is no longer valid when the coupling constants get large, and (2) $10^{34}$ GeV is well beyond the Planck scale, so that ignoring the effects of (quantum) gravity is not valid.

If there is a Landau pole (or failure of a coupling constant to tend to zero at high energy scales) in the standard model, it would appear first in the scalar quartic coupling $\lambda$ -- but the requirement that $\lambda$ and the Yukawa couplings do not blow up before the Planck scale puts useful constraints on particle masses. See, for example,

N. Cabibbo, L. Maiani, G. Parisi, R. Petronzio. Nucl. Phys., B136 (1978) [doi:10.1016/0550-3213(79)90167-6]

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