1. The action for bulk and brane

• Bulk action:

  • ungauged part (8 supersymmetries)
  • gauged part: with coupling constant g

• Replace g by G(x), which, by a Lagrange multiplier field, is put equal to a constant

• Brane action has extra terms for the Lagrange multiplier D-1 form, allowing g to vary crossing the brane

In every step supersymmetry is preserved !

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