The problem of nonlocality in string theory

Abstract

We discuss the problems associated with the essential nonlocality of all string field actions. Manifestly Poincaré invariant theories are shown to be unstable and bereft of an initial value formulation; light cone theories suffer from a breakdown of Lorentz invariance. However, because free string actions are local up to a field redefinition these problems are invisible to perturbative analysis. The use of perturbation theory is shown to change the causal and canonical structure of the covariant formulations. One consequence is the loss of the infinite number of nonperturbative solutions associated with the freedom to prescribe arbitrarily many initial time derivatives. Since these solutions also contain the negative energy degrees of freedom which destabilize the theory both covariant problems are avoided in this way. The penalty is acausality. This is fundamental property of the light cone formalism. It can be avoided in the covariant theory only by restoring the nonperturbative solutions.