Stringy Fuzziness as the Custodian of Time-Space Noncommutativity

TL;DR

This paper investigates the limitations of achieving noncommuting time-space coordinates in string theory, revealing an obstruction linked to string fuzziness and causality, and explores related supergravity solutions with singularities.

Contribution

It identifies an obstruction in decoupling time-space noncommutativity from string fuzziness within standard backgrounds and analyzes the associated supergravity geometry.

Findings

Obstruction prevents decoupling of noncommutativity scale from string fuzziness.

Supergravity solutions exhibit naked singularities at noncommutativity scales.

Complex dilaton values can formally achieve decoupling, akin to black-hole horizons.

Abstract

We study aspects of obtaining field theories with noncommuting time-space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed-string backgrounds, there is an obstruction to decoupling the time-space noncommutativity scale from 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 closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally 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 horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity.