Deformations of Superconformal Theories

TL;DR

This paper classifies all possible supersymmetry-preserving deformations of superconformal theories in dimensions three and higher, revealing how these deformations affect the theories' structure and constraints.

Contribution

It provides a symmetry-based, model-independent classification of relevant, marginal, and irrelevant deformations without requiring a Lagrangian.

Findings

Many theories admit deformations in multiplets with conserved currents.

Some theories with high supersymmetry have no relevant or marginal deformations.

Irrelevant deformations impose new constraints on moduli-space effective actions.

Abstract

We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.