On Supersymmetry, Boundary Actions and Brane Charges

Understand

Supersymmetry transformations change the Lagrangian $\mathscr{L}$ into a total derivative $\delta \mathscr{L} = \partial_\mu \mathcal{V}^{\mu}$.

• On manifolds with boundaries the total derivative term is an obstruction to preserving supersymmetry.
• Such total derivative terms can be canceled by a boundary action without specifying boundary conditions, but only for a subalgebra of supersymmetry.
• We study compensating boundary actions for $\mathcal{N}=1$ supersymmetry in 4d, and show that they are determined independently of the details of the theory and of the boundary conditions.