Twisted supersymmetry and the topology of theory space

TL;DR

This work studies four-dimensional gauge theories organized as theory spaces (sites and links) and shows that topology can govern supersymmetry breaking. By introducing a global phase twist in the couplings, SUSY breaking becomes nonlocal in theory space and is suppressed by $(\alpha/4\pi)^N$, with stronger suppression in Abelian and non-Abelian quiver theories; in regions where theory space yields an emergent extra dimension, the breaking reduces to Scherk-Schwartz boundary-condition breaking. The authors develop a homology-based framework to classify local SUSY and obstructions to removing phases, and illustrate with circular, ribbon, and RP^2-like theory spaces. They extend the construction to ${\cal N}=2$ theories, showing possible preservation of ${\cal N}=1$ or full ${\cal N}=0$ depending on the twist, including walking gauge behavior from nonzero wave-function renormalization. Overall, the paper provides a UV-complete perspective on Scherk-Schwartz breaking via theory-space topology and discusses potential phenomenological applications, such as hidden-sector SUSY breaking and improved unification scenarios.

Abstract

We present examples of four dimensional, non-supersymmetric field theories in which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings and the vacuum energy, are suppressed by $(α/4 π)^{N}$, where $α$ is a weak coupling factor and $N$ can be made arbitrarily large. The particle content and interactions of these models are conveniently represented by a graph with sites and links, describing the gauge theory space structure. While the theories are supersymmetric ``locally'' in theory space, supersymmetry can be explicitly broken by topological obstructions.

Figures (6)

• Figure 1: Theory space for a $U(1)^N$ model.
• Figure 2: The leading diagram contributing to the vacuum energy.
• Figure 3: The same as fig. 2 for a non-Abelian theory.
• Figure 4: Ribbon theory space
• Figure 5: A non-local theory space.