Twisted supersymmetry and the topology of theory space

TL;DR

This paper constructs four-dimensional non-supersymmetric field theories where supersymmetry breaking effects are highly suppressed, using a graph-based theory space structure that allows local supersymmetry but global breaking via topology.

Contribution

It introduces a novel framework for suppressing supersymmetry breaking effects through topological obstructions in a graph-structured theory space.

Findings

Supersymmetry breaking effects are suppressed by a factor of $(rac{ ext{alpha}}{4\pi})^{N}$.

Models are represented by a graph with sites and links, encoding gauge interactions.

Supersymmetry can be broken explicitly by topological obstructions despite local supersymmetry.

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 $(\alpha/4 \pi)^{N}$, where $\alpha$ 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.