Cosmological Constant in Low Energy $d = 4$ String Leads to Naked Singularity

Abstract

In the sigma model approach, the $β$-function equations for non critical strings contain a term which acts like a tree level cosmological constant, $Λ$. We analyse the static, spherically symmetric solutions to these equations in $d = 4$ space time and show that the curvature scalar seen by the strings is singular if $Λ\ne 0$. This singularity is naked. Requiring its absence in our universe imposes the constraint $| Λ| < 10^{- 120}$ in natural units. {}From another point of view, our analysis implies that low energy $d = 4$ non critical strings lead to naked singularities.