Closed Strings in Misner Space: Cosmological Production of Winding Strings

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 work, the study of weakly coupled closed strings on this space is pursued in several directions: (i) physical states in the twisted sectors are found to come in two kinds: short strings, which wind along the compact space-like direction in the cosmological (Milne) regions, and long strings, which wind along the compact time-like direction in the (Rindler) whiskers. The latter can be viewed as infinitely long static open strings, stretching from Rindler infinity to a finite radius and folding back onto themselves. (ii) As in the Schwinger effect, tunneling between these states corresponds to local pair production of winding strings. The tunneling rate approaches unity as the winding number $w$ gets large, as a consequence of the singular geometry. (iii) The one-loop string amplitude has singularities on the moduli space, associated to periodic closed string trajectories in Euclidean time. In the untwisted sector, they can be traced to the combined existence of CTCs and Regge trajectories in the spectrum. In the twisted sectors, they indicate pair production of winding strings. (iv) At a classical level and in sufficiently low dimension, the condensation of winding strings can indeed lead to a bounce, although the required initial conditions are not compatible with Misner geometry at early times. (v) The semi-classical analysis of winding string pair creation can be generalized to more general (off-shell) geometries. We show that a regular geometry regularizes the divergence at large winding number.Comment: 46 pages, 5 figures, uses JHEP3.cls; v2: title changed and other minor improvements, final version to appear in JCA

Closed Strings in Misner Space: Stringy Fuzziness with a Twist

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 $\sqrt{\log w}$, which can be much larger than the string scale. Wave functions are smeared by an operator $\exp(\Delta(\nu) \partial_+ \partial_-)$ reminiscent of the Moyal-product of non-commutative geometry, which, since $\Delta(\nu)$ 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.Comment: 29 pages, Latex2e, uses JHEP3.cls; v3: minor corrections, final version to appear in JCA

On Schwinger Pair Creation in Gravity and in Closed Superstring Theory

We investigate the Schwinger pair creation process in the context of gravitational models with the back reaction of the electric field included in the geometry. The background is also an exact solution of type II superstring theory, where the electric field arises by Kaluza-Klein reduction. We obtain a closed formula for the pair creation rate that incorporates the gravitational back reaction. At weak fields it has the same structure as the general Schwinger formula, albeit pairs are produced by a combination of Schwinger and Unruh effect, the latter due to the presence of a Rindler horizon. In four spacetime dimensions, the rate becomes constant at strong electric fields. For states with mass of Kaluza-Klein origin, the rate has a power-like dependence in the electric field, rather than the familiar (non-perturbative) exponential dependence. We also reproduce the same formula from the string partition function for winding string states. Finally, we comment on the generalization to excited string states.Comment: 21 page

Matrix Description of Interacting Theories in Six Dimensions

We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of $N$ instantons in \IR^4.Comment: 10 pages, harvmac bi

The abelian cosets of the Heisenberg group

In this paper we study the abelian cosets of the H(4) WZW model. They coincide or are related to several interesting three-dimensional backgrounds such as the Melvin model, the conical point-particle space-times and the null orbifold. We perform a detailed CFT analysis of all the models and compute the coset characters as well as some typical three-point couplings of coset primaries.Comment: 26 pages; v2: minor typos corrected, also added section 3.3 and 4.3 with a few comments on a third class of geometries that have not been discussed in v

D-instantons and Closed String Tachyons in Misner Space

We investigate closed string tachyon condensation in Misner space, a toy model for big bang universe. In Misner space, we are able to condense tachyonic modes of closed strings in the twisted sectors, which is supposed to remove the big bang singularity. In order to examine this, we utilize D-instanton as a probe. First, we study general properties of D-instanton by constructing boundary state and effective action. Then, resorting to these, we are able to show that tachyon condensation actually deforms the geometry such that the singularity becomes milder.Comment: 24 pages, 1 figure, minor change