The uniqueness of the abelian Born-Infeld action

Starting from BPS solutions to Yang-Mills which define a stable holomorphic vector bundle, we investigate its deformations. Assuming slowly varying fi eldstrengths, we find in the abelian case a unique deformation given by the abelian Born-Infled action. We obtain the deformed Donaldson-Uhlenbeck-Yau stability condition to all orders in alpha '. This result provides strong evidence supporting the claim that the only supersymmetric deformation of t he abelian d = 10 supersymmetric Yang-Mills action is the Born-Infeld actio n. (C) 2001 Elsevier Science B.V. All rights reserved.