Supersymmetric composite models

Abstract

A review of the formation of massless composite spin- 1 2 states within supersymmetric gauge theories is presented. It is hoped that a phenomenologically successful supersymmetric composite model of quarks and leptons will emerge from this research program. Two principal scenarios are reviewed: (i) massless composite fermion formation due to an exact chiral symmetry ('t Hooft consistency conditions), and (ii) massless composite fermions as the supersymmetric partners of composite Goldstone bosons (composite quasi-Goldstone fermions) arising from the dynamical breaking of chiral symmetry. Section 2 begins with reviews of: the elements of anomaly theory, the anomaly-matching equations, decoupling and the persistent mass condition, anomaly matching in QCD and the supergroup classification of solutions. Then the 't Hooft anomaly-matching equations and decoupling à la 't Hooft are used to study a wide range of theories that assume exact chiral symmetry. It is shown that the presence of an exact R-symmetry (before considering the axial anomaly) greatly restricts the space of solutions in many models. The inclusion of the gauge supermultiplet as an important ingredient in the composite spectrum introduces more freedom. However, an investigation of the properties of the solutions does not yield an obviously viable composite model. Solutions obtained when R-symmetry is hypothesized to be dynamically broken are also examined. The Goldstone mechanism in supersymmetric theories, non-linear realizations, effective lagrangians (supersymmetric σ-models) and Kähler geometry are discussed in section 3. These techniques are then used to survey quasi-Goldstone fermion models. Theories based on unitary groups are discussed first; the topics covered include the novino model and mechanism, the dynamical breaking of SU(2) L, the interplay between anomaly matching and the Goldstone mechanism, and two-scale models. Finally, models based on exceptional groups are examined. A conclusion is then presented, together with a discussion of future research possibilities.