Quantum string theory effective action

Abstract

We present a covariant background field method for quantum string dynamics. It is based on the effective action Γ for fields corresponding to different string modes. A formalism is developed for the calculation of Γ in the α′ → 0 limit. It is shown that in the case of closed Bose strings Γ contains the standard kinetic terms for the scalar, external metric and the antisymmetric tensor. Our approach makes possible a consistent formulation and solution of a ground state problem (including the problem of space-time compactification) in the string theory. We suggest a solution to the old “tachyon problem” based on the generation of non-trivial vacuum values for the scalar field, metric and antisymmetric tensor. It is shown that a preferred compactification in the closed Bose string theory is to three (anti-de Sitter) space-time dimensions.