Perturbative Calculations in the Effective Lagrangian and $2D$ Closed String Field Theory

Abstract

This paper is devoted to the study of closed string field theory in two dimensions. We compare two different approaches: BRST closed string field theory and the string effective Lagrangian. We show that the quadratic action and the pole structures of tree-level scattering amplitudes agree. We study merits and drawbacks of various gauge fixing procedures. In particular, we discuss conformal gauge in the context of the effective Lagrangian, and Siegel and Lorentz-like gauge in the general BRST approach. We discuss the ways in which discrete states survive a particular gauge fixing both by directly solving the equations of motion, and by analyzing pole structure of the scattering amplitudes.