The Uniqueness of the Abelian Born-Infeld Action

TL;DR

This paper demonstrates that the abelian Born-Infeld action uniquely deforms supersymmetric Yang-Mills solutions, maintaining stability conditions and supporting its role as the sole supersymmetric deformation in this context.

Contribution

It proves the uniqueness of the abelian Born-Infeld action as the deformation of supersymmetric Yang-Mills theory under certain assumptions.

Findings

The deformation aligns with the abelian Born-Infeld action.

The deformed stability condition holds to all orders in alpha'.

Supports the conjecture that Born-Infeld is the only supersymmetric deformation.

Abstract

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 alpha'. 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.