The Higgs effective potential in non-Abelian gauge-Higgs unification on M4 x S1 is finite at two loops, but in an M5 x S1 example it depends on a four-Fermi counterterm at three loops.
Two-loop Calculation of Higgs Mass in Gauge-Higgs Unification: 5D Massless QED Compactified on S^1
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abstract
We calculate the quantum corrections to the mass of the zero mode of the fifth component of the gauge field at two-loop level in a five dimensional massless QED compactified on S^1. We discuss in detail how the divergences are exactly canceled and the mass becomes finite. The key ingredients to obtain the result are the five dimensional gauge invariance and the Ward-Takahashi identity. We also evaluate the finite part of corrections.
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To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification
The Higgs effective potential in non-Abelian gauge-Higgs unification on M4 x S1 is finite at two loops, but in an M5 x S1 example it depends on a four-Fermi counterterm at three loops.