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

Abstract

In the sigma model approach, the $\beta$-function equations for non critical strings contain a term which acts like a tree level cosmological constant, $\Lambda$. 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 $\Lambda \ne 0$. This singularity is naked. Requiring its absence in our universe imposes the constraint $|\Lambda |<10^{-120}$ in natural units. {}From another point of view, our analysis implies that low energy $d=4$ non critical strings lead to naked singularities.

13 pages, preprint TCD-1-94. Revised version: a note and some references added; a few minor changes in the text

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