Rigid supersymmetry with boundaries

TL;DR

The article develops a systematic framework for rigid supersymmetry in the presence of timelike boundaries by constructing bulk-plus-boundary actions that preserve half of the bulk SUSY through extended $F$- and $D$-term formulas in $3$- and $4$-dimensional theories. It shows how to realize "susy without BC" in several models (3D and 4D Wess-Zumino, Maxwell, and Chern-Simons) and when additional separately SUSY boundary actions, often built from co-dimension one boundary superfields, are required to cancel boundary terms linear in auxiliary fields. The authors also analyze the Euler-Lagrange variation to reveal the orbit of boundary conditions compatible with SUSY, and they demonstrate the equivalence of tensor-calculus and superspace approaches, including explicit co-dimension one projections. The results have potential applications in brane and higher-dimensional SUSY constructions, AdS/CFT, and Horava-Witten-type scenarios, where boundaries and auxiliary fields play crucial roles.

Abstract

We construct rigidly supersymmetric bulk-plus-boundary actions, both in $x$-space and in superspace. For each standard supersymmetric bulk action a minimal supersymmetric bulk-plus-boundary action follows from an extended $F$- or $D$-term formula. Additional separately supersymmetric boundary actions can be systematically constructed using co-dimension one multiplets (boundary superfields). We also discuss the orbit of boundary conditions which follow from the Euler-Lagrange variational principle.