On Solvable Time-Dependent Model and Rolling Closed String Tachyon

TL;DR

This paper analyzes a solvable time-dependent string theory background modeled by the SL(2,R)/U(1) WZW model at level 0<k<2, exploring its metric, wave functions, and string interactions, providing insights into closed string tachyon dynamics.

Contribution

It presents an exact analysis of a time-dependent string background, including computations of correlation functions and vacuum amplitude, linking Euclidean and Lorentzian models.

Findings

Exact metric and wave functions derived

Two and three point functions computed

Relation between Euclidean and Lorentzian models clarified

Abstract

We investigate the SL(2,R)/U(1) WZW model with level 0<k<2 as a solvable time-dependent background in string theory. This model is expected to be dual to the one describing a rolling closed string tachyon with a time-like linear dilaton. We examine its exact metric and minisuperspace wave functions. Two point functions and the one-loop vacuum amplitude are computed and their relation to the closed string emission is discussed. Comparing with the results from the minisuperspace approximation, we find a physical interpretation of our choice to continue the Euclidean model into the Lorentzian one. Three point functions are also examined.