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.
Highlights
In this paper we consider unitary superconformal field theories (SCFTs) in 3 ≤ d ≤ 6 spacetime dimensions.1 Our main result is a classification of their possible relevant, irrelevant, and marginal operator deformations that preserve the non-conformal Poincare supersymmetries and Lorentz invariance, but not necessarily conformal symmetry
Its existence invalidates the standard lore that supersymmetric deformations necessarily reside at the highest level of a multiplet. (As we will explain in section 2, this lore is correct for suitably generic multiplets.) Similar universal mass deformations, which reside in the middle of stress-tensor multiplets, exist in three-dimensional theories with N ≥ 5 supersymmetry
The main result of this paper is a classification of all Lorentz-invariant, supersymmetric deformations that can arise for SCFTs in 3 ≤ d ≤ 6 dimensions
Summary
In this paper we consider unitary superconformal field theories (SCFTs) in 3 ≤ d ≤ 6 spacetime dimensions. Our main result is a classification of their possible relevant, irrelevant, and marginal operator deformations that preserve the non-conformal Poincare supersymmetries and Lorentz invariance, but not necessarily conformal symmetry. In this paper we consider unitary superconformal field theories (SCFTs) in 3 ≤ d ≤ 6 spacetime dimensions.. Our main result is a classification of their possible relevant, irrelevant, and marginal operator deformations that preserve the non-conformal Poincare supersymmetries and Lorentz invariance, but not necessarily conformal symmetry. These deformations are tabulated, which is self-contained. The classification utilizes the fact that the deforming operators reside in unitary representations of the superconformal symmetry, which are much more constrained that representations of Poincare supersymmetry.. Since we only rely on general properties of these representations, our results are model independent and do not require a Lagrangian The classification utilizes the fact that the deforming operators reside in unitary representations of the superconformal symmetry, which are much more constrained that representations of Poincare supersymmetry. Since we only rely on general properties of these representations, our results are model independent and do not require a Lagrangian
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
