Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects

TL;DR

This paper investigates four-dimensional superconformal theories with three-dimensional boundaries or defects, demonstrating their superconformal invariance at all orders and analyzing a specific N=4 Yang-Mills model with a defect, confirming its conformality.

Contribution

The authors construct and analyze superconformal boundary/defect models in 4D theories, proving their invariance and conformality at all perturbative orders, and clarify the superspace formulation of a notable N=4 model.

Findings

Beta functions vanish to all orders, ensuring superconformal invariance.

The N=4 SU(N) Yang-Mills with defect is conformal, supported by superspace analysis.

Non-renormalization theorems make the conformality of the defect model transparent.

Abstract

We study four-dimensional superconformal field theories coupled to three-dimensional superconformal boundary or defect degrees of freedom. Starting with bulk N=2, d=4 theories, we construct abelian models preserving N=2, d=3 supersymmetry and the conformal symmetries under which the boundary/defect is invariant. We write the action, including the bulk terms, in N=2, d=3 superspace. Moreover we derive Callan-Symanzik equations for these models using their superconformal transformation properties and show that the beta functions vanish to all orders in perturbation theory, such that the models remain superconformal upon quantization. Furthermore we study a model with N=4 SU(N) Yang-Mills theory in the bulk coupled to a N=4, d=3 hypermultiplet on a defect. This model was constructed by DeWolfe, Freedman and Ooguri, and conjectured to be conformal based on its relation to an AdS configuration studied by Karch and Randall. We write this model in N=2, d=3 superspace, which has the distinct advantage that non-renormalization theorems become transparent. Using N=4, d=3 supersymmetry, we argue that the model is conformal.