Vacuum States in 2D Tachyon Effective Action

In this paper we will study the ground states of the toy model of 2D closed string tachyon effective action. We will firstly construct the classical solutions of the tachyon effective action that do not induce backreaction on metric and dilaton. Then we will study the quantum mechanics of the zero mode of the tachyon field. We will find family of vacuum states labelled with single parameter. We will also perform the quantum mechanical analysis of the tachyon effective action when we take into account dynamics of nonzero modes. We will calculate the vacuum expectation values of components of the stress energy tensor and dilaton source and we will argue that there is not any backreaction on metric and dilaton.