Born-Infeld theory with higher derivatives

Abstract

We present new models of nonlinear electromagnetism which satisfy the Noether-Gaillard-Zumino current conservation and are, therefore, self-dual. The new models differ from the Born-Infeld--type models in that they deform the Maxwell theory starting with terms like $\ensuremath{\lambda}(\ensuremath{\partial}F{)}^{4}$. We provide a recursive algorithm to find all higher-order terms in the action of the form ${\ensuremath{\lambda}}^{n}{\ensuremath{\partial}}^{4n}{F}^{2n+2}$, which are necessary for the $U(1)$ duality current conservation. We use one of these models to find a self-dual completion of the $\ensuremath{\lambda}(\ensuremath{\partial}F{)}^{4}$ correction to the open string action. We discuss the implication of these findings for the issue of UV finiteness of $\mathcal{N}=8$ supergravity.