A Bulk Effect to SUSY Effective Potential in a 5D Super-Yang-Mills Model

TL;DR

This paper estimates the one-loop supersymmetric effective potential in a 5D super-Yang-Mills model compactified on an interval, revealing a bulk effect that stabilizes the extra dimension at an intermediate mass scale.

Contribution

It provides a novel calculation of the 1-loop effective potential including Kaluza-Klein modes and demonstrates a mechanism for stabilizing the size of the extra dimension.

Findings

Effective potential exhibits linear growth with cutoff due to Kaluza-Klein modes.

The size of the extra dimension is stabilized at an intermediate scale of 10^{12-14} GeV.

Bulk effects significantly influence the stabilization of extra dimensions.

Abstract

Supersymmetric effective potential of a 5D super-Yang-Mills model compactified on $S^1/Z_2$, i.e., on an interval $l$ of extra dimension, is estimated at the 1-loop level by the auxiliary field tadpole method. For the sake of infinite towers of Kaluza-Klein excitation modes of bulk fields involved in the tadpoles, there arises a definite bulk effect of linear growth of the effective potential along with the cutoff ${\mit\Lambda}$ which is greatly suppressed by $l$ to produce finite contributions. The minimization of the effective potential incorporating the tree potential and a Fayet-Iliopoulos $D$-term reveals an interesting case that the size of $l$ is stabilized at a length corresponding to an intermediate mass scale $10^{12-14}$ GeV.