A premier analysis of supersymmetric closed string tachyon cosmology

Abstract

Abstract. From a previously found worldline supersymmetric formulation for the effective action of the closed string tachyon in a FRW background, the Hamiltonian of the theory is constructed, by means of the Dirac procedure, and written in a quantum version. Using the supersymmetry algebra we are able to find solutions to the Wheeler-DeWitt equation via a more simple set of first order differential equations. Finally, for the k = 0 case, we compute the expectation value of the scale factor with a suitably potential also favored in the present literature. We give some interpretations of the results and state future work lines on this matter. IntroductionTachyons correspond to the lowest mode of string theory, which for the lack of knowledge on how to handle unstable configurations were ignored for many years. With the inclusion of supersymmetry they can be consistently eliminated from the spectrum by the GSO truncation. Some years ago it has been seen that the evolution of these tachyonic instabilities can be described by the condensation of the tachyonic modes. This was first perfomed in the simpler case of open strings, resumed by the well known Sen conjectures [1]. Whereas for closed strings the situation is more complicated, because it involves the structure of space-time. A key element for the development of the present work is the interesting fact that closed string tachyons, which are nonsupersymmetric in the target space, can have worldsheet supersymmetry [2]. Supersymmetric cosmology has been studied in a variety of different schemes, we refer the interested reader to the well known books by D'Eath and Moniz for a review [3,4]. In [5] a Lagrangian of supersymmetric tachyons in the framework of a FRW background was given in a worldline superspace where, the time variable is extended to the superspace of supersymmetry [6,7], this is done considering the covariant formulation of one-dimensional supergravity of the so called 'new ' Θ variables [8, 9], which allows in a straightforward way to write supergravity invariant actions. The present work is performed along such approach, we depart from the Hamiltonian given in [5], then we give a particular, and normalizable, solution to the WheelerDeWitt equation via the superalgebra constraints, which act as square roots of the WDW equation. We compute the scale factor expectation value as customary. Plots of the results are given, follow up by some conclusions and final remarks on future work.