Two-loop calculation of Higgs mass in gauge-Higgs unification: 5D massless QED compactified on S1S1

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 S1S1. We discuss in detail how the divergences are exactly canceled and the mass becomes finite. The key ingredients to obtain the result are the shift symmetry and the Ward–Takahashi identity. We also evaluate the finite part of corrections.