Abstract
We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification.
Highlights
Flux compactificationLet us first consider a six-dimensional U(1) gauge theory with a constant magnetic flux
No signature of new physics has been found, which is likely to increase the new physics scale, namely Higgs mass
We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification
Summary
Let us first consider a six-dimensional U(1) gauge theory with a constant magnetic flux. The magnetic flux is given by the nontrivial background (or vacuum expectation value (VEV)) of the fifth and the sixth component of the gauge field A5,6. This background must satisfy their classical equation of motion ∂m Fmn = 0. Which introduces a constant magnetic flux density F56 = f with a real number f. Note that this solution breaks an extra-dimensional translational invariance spontaneously. We define the covariant derivatives in the complex coordinates as follows
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