Supersymmetry in Field Theory

TL;DR

This paper reviews supersymmetric field theories, emphasizing their role in addressing the gauge hierarchy problem and discussing recent nonperturbative insights gained through holomorphy and symmetry principles.

Contribution

It provides a comprehensive overview of supersymmetry in field theories, including its formulation, relation to space-time symmetry, and recent advances in nonperturbative analysis.

Findings

Supersymmetry unifies bosons and fermions within relativistic frameworks.

Holomorphy and symmetry arguments have led to breakthroughs in nonperturbative studies.

Supersymmetric theories offer solutions to the gauge hierarchy problem.

Abstract

Supersymmetric theories are reviewed in the context of field theories. The gauge hierarchy problem in attempting the unification of all fundamental interactions is the strongest motivation of modern development of supersymmetry. Starting from the general notion of supersymmetry as a symmetry between bosons and fermions, we explain how the supersymmetry becomes a part of the space-time symmetry if we wish to maintain the relativisitic invariance. The precise idea of supersymmetry is then introduced and the supersymmetric field theories are formulated. There has been a significant breakthrough in the study of nonperturbative effects in supersymmetric field theories using the holomorphy and symmetry arguments. Some of these ideas and results are briefly reviewed.