Supersymmetric Theories on a Non Simply Connected Space-Time

TL;DR

This paper investigates the Wess-Zumino supersymmetric theory on a compactified space-time, demonstrating conditions under which the vacuum energy vanishes and analyzing the nonanalytic behavior of two-point functions at one loop.

Contribution

It provides a detailed analysis of supersymmetric theories on non simply connected space-times, highlighting conditions for vacuum stability and the structure of quantum corrections.

Findings

Vacuum energy vanishes when bosonic and fermionic fields share boundary conditions.

Two-point functions are consistent with nonrenormalization theorems.

Nonanalyticity in two-point functions is identified and discussed.

Abstract

We study the Wess-Zumino theory on ${\bf R}^3 \times S^1$ where a spatial coordinate is compactified. We show that when the bosonic and fermionic fields satisfy the same boundary condition, the theory does not develop a vacuum energy or tadpoles. We work out the two point functions at one loop and show that their forms are consistent with the nonrenormalization theorem. However, the two point functions are nonanalytic and we discuss the structure of this nonanalyticity.