Misner space, also known as the Lorentzian orbifold R 1,1 /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 √ log w, which can be much larger than the string scale. Wave functions are smeared by an operator exp (∆(ν)∂ + ∂ − ) reminiscent of the Moyal-product of non-commutative geometry, which, since ∆(ν) is real, modulates the amplitude rather than the phase of the wave function, 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 in principle to compute, to leading order, the back-reaction on the metric due to a condensation of coherent winding strings. * Incumbent of the Recanati career development chair for energy research Contents

Misner space, also known as the Lorentzian orbifold R 1,1 /boost, is one of the simplest examples of a cosmological singularity in string theory. In this lecture, we review the semi-classical propagation of closed strings in this background, with a particular emphasis on the twisted sectors of the orbifold. Tree-level scattering amplitudes and the one-loop vacuum amplitude are also discussed.Thus I was moving along the sloping curve of the time loop towards that place in which the Friday me before the beating would change into the Friday me already beaten. I. Tichy, [1]Despite their remarkable success in explaining a growing body of high precision cosmological data, inflationary models, just as the Hot Big Bang Model, predict an Initial Singularity where effective field theory ceases to be valid [2]. As a quantum theory of gravity, String Theory ought to make sense even in this strongly curved regime, possibly by providing an initial quantum state if the Initial Singularity is truely an Origin of Time, or by escaping it altogether if stringy matter turns out to be less prone to gravitational collapse than conventional field-theoretic matter. Unfortunately, describing cosmological singularities and, less ambitiously, time dependence in string theory has been *