Stringy fuzziness as the custodian of time-space noncommutativity

We study aspects of obtaining field theories with noncommuting time-space c oordinates as limits of open-string theories in constant electric-field bac kgrounds. We find that, within the standard closed-string backgrounds, ther e is an obstruction to decoupling the time-space noncommutativity scale fro m that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure . We study the moduli space of the obstruction in terms of the open- and cl osed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved fo rmally by considering complex values of the dilaton and inverting the role of space and time in the: light cone. This is reminiscent of a black-hole h orizon. We study the corresponding supergravity solution in the large-N lim it and find that the geometry has a naked singularity at the physical scale of noncommutativity. (C) 2000 Elsevier Science B.V. All rights reserved.