The uniqueness of the abelian Born–Infeld action Original Research Article

Starting from BPS solutions to Yang–Mills which define a stable holomorphic vector bundle, we investigate its deformations. Assuming slowly varying fieldstrengths, we find in the abelian case a unique deformation given by the abelian Born–Infeld action. We obtain the deformed Donaldson–Uhlenbeck–Yau stability condition to all orders in α′. This result provides strong evidence supporting the claim that the only supersymmetric deformation of the abelian d=10 supersymmetric Yang–Mills action is the Born–Infeld action.