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. (C) 2000 Elsevier Science B.V.
Misner space, also known as the Lorentzian orbifold R-1,R-1/ boost, is the simplest tree-level solution of string theory with a cosmological singularity. We compute tree-level scattering amplitudes involving twisted states, using operator and current algebra techniques. We find that, due to zero-point quantum fluctuations of the excited modes, twisted strings with a large winding number w are fuzzy on a scale rootlog w, which can be much larger than the string scale. Wavefunctions are smeared by an operator exp(Delta(nu)partial derivative(+)partial derivative(-)) reminiscent of the Moyal product of non-commutative geometry, which, since Delta(nu) is real, modulates the amplitude rather than the phase of the wavefunction, and is purely gravitational in its origin. We compute the scattering amplitude of two twisted states and one tachyon or graviton, and find a finite result. The scattering amplitude of two twisted and two untwisted states is found to diverge, due to the propagation of intermediate winding strings with vanishing boost momentum. The scattering amplitude of three twisted fields is computed by analytic continuation from three-point amplitudes of states with non-zero p(+) in the Nappi-Witten plane wave, and the non-locality of the three-point vertex is found to diverge for certain kinematical configurations. Our results for the three-point amplitudes allow us in principle to compute, to leading order, the back-reaction on the metric due to a condensation of coherent winding strings.
We study nonanticommutative deformations of N = 2 two-dimensional euclidean sigma models. We find that these theories are described by simple deformations of Zumino's lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.