Nonvanishing Finite Scalar Mass in Flux Compactification

TL;DR

This paper demonstrates the possibility of achieving a nonzero finite Wilson line scalar mass in flux compactifications, providing explicit examples and conditions for finiteness in quantum corrections.

Contribution

It generalizes loop integral conditions for finiteness and presents the first explicit example of finite Wilson line scalar mass in flux compactification.

Findings

Derived conditions for finiteness of loop integrals and mode sums.

Classified interaction terms satisfying finiteness conditions.

Explicitly computed finite Wilson line scalar mass in 6D scalar QED.

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.