2011/03/11 by Adel Bilal
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Invariant (physics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Sigma #Submanifold #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep11(2011)046
38 pages, 1 figure
arxiv created 2011/03/11 · openalex publication_date 2011/11/01 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We make a comprehensive study of (rigid) N = 1 supersymmetric sigma-models with general Kähler potentials K and superpotentials w on four-dimensional space-times with boundaries. We spell out the minimal (non-supersymmetric) boundary terms one must add to the standard bulk action to make it off-shell invariant under half the supersymmetries without imposing any boundary conditions. Susy boundary conditions do arise from the variational principle when studying the dynamics. Upon including an additional boundary action that depends on an arbitrary real boundary potential B one can generate very general susy boundary conditions. We show that for any set of susy boundary conditions that define a Lagrangian submanifold of the Kähler manifold, an appropriate boundary potential B can be found. Thus the non-linear sigma-model on a manifold with boundary is characterised by the triple (K, B, w). We generalize our results to supersymmetric junctions between completely different susy sigma-models, living on adjacent domains and interacting through a “permeable” wall. We obtain the supersym-metric matching conditions that allow us to couple models with different Kähler potentials and superpotentials on each side of the wall.