Deformations of Superconformal Theories (1602.01217v1)

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.

• The paper classifies relevant, marginal, and irrelevant deformations in unitary SCFTs across three to six dimensions using symmetry and unitarity methods.
• It finds that deformations often coexist with conserved currents, occasionally appearing sporadically within multiplets and modifying the supersymmetry algebra.
• The study constrains effective actions and opens research directions on universal mass deformations and exactly marginal operators in various SCFTs.

Overview of "Deformations of Superconformal Theories"

The paper "Deformations of Superconformal Theories," authored by Clay Córdova, Thomas T. Dumitrescu, and Kenneth Intriligator, presents a comprehensive classification of possible deformations in unitary superconformal field theories (SCFTs) across three to six spacetime dimensions. By focusing on model-independent results derived from symmetries and unitarity rather than Lagrangian descriptions, the authors explore how deformations can preserve the non-conformal Poincaré supersymmetries and Lorentz invariance.

Key Findings

1. Classification of Deformations:
   • The paper examines relevant, marginal, and irrelevant deformations across various dimensionalities and grades of supersymmetry.
   • A notable insight is that theories with enough supersymmetry might lack relevant or marginal deformations entirely, rendering them isolated.
2. Multiplet Structures:
   • Many SCFTs have deformations residing in multiplets alongside conserved currents. These deformations often affect the supersymmetry algebra by introducing charges.
   • Surprisingly, some deformations appear in the middle of a multiplet—a phenomenon termed "sporadic"—contradicting the usual expectation that top-components only appear at the highest level.
3. Specific Dimensional Insights:
   • For instance, in three-dimensional theories, SCFTs with $\mathcal{N}\geq4$ admit universal mass deformations that lead to non-trivial modifications of the supersymmetry algebra. In four dimensions, $\mathcal{N}=4$ theories universally feature an exactly marginal deformation related to the stress-tensor multiplet.

Implications for Future Research

• Constraints on Effective Actions: The classification provides constraints on moduli-space effective actions, including potential metrics and terms dictated by supersymmetry structures. Understanding these constraints is crucial for theorists aiming to develop comprehensive and accurate models in superconformal contexts.
• Exploration of Sporadic Phenomena: The sporadic appearance of deformations within multiplets opens new pathways for exploration, potentially revealing deeper insights into the structure and behavior of superconformal theories.
• Supersymmetry Algebra Modifications: The paper highlights the unique situations where supersymmetry algebra receives modifications, challenging conventional understanding and potentially leading to novel theories that account for such phenomena.

Conclusion

This paper serves as a pivotal reference for those researching the constraints and possibilities within superconformal theories. By delineating the effects of various deformations on SCFTs, it sets the stage for more comprehensive studies on the implications of supersymmetry in quantum field theories. Future research into these areas could significantly impact the theoretical landscape of higher dimensional superconformal theories and the unified theories that might emerge from them.