Correct Effective Potential of Supersymmetric Yang-Mills Theory on M^4\times S^1

TL;DR

This paper accurately computes the one-loop effective potential for supersymmetric Yang-Mills theory on M^4×S^1, incorporating vacuum expectation values and supersymmetry breaking mechanisms, leading to insights on gauge symmetry breaking and mass generation.

Contribution

It provides a corrected and comprehensive calculation of the effective potential including scalar VEVs and supersymmetry breaking effects, extending previous analyses.

Findings

Vacuum expectation values significantly influence the effective potential.

Large supersymmetry breaking increases scalar masses.

Masses for scalars and gauge components are explicitly derived for SU(2).

Abstract

We study an ${\cal N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$. The vacuum expectation values for adjoint scalar field in vector multiplet, though important, has been overlooked in evaluating one-loop effective potential of the theory. We correctly take the vacuum expectation values into account in addition to the Wilson line phases to give an expression for the effective potential, and gauge symmetry breaking is discussed. In evaluating the potential, we employ the Scherk-Schwarz mechanism and introduce bare mass for gaugino in order to break supersymmetry. We also obtain masses for the scalars, the adjoint scalar, and the component gauge field for the $S^1$ direction in case of the SU(2) gauge group. We observe that large supersymmetry breaking gives larger mass for the scalar. This analysis is easily applied to the $M^4\times S^1/Z_2$ case.