Divergences of Discrete States Amplitudes and Effective Lagrangian in 2D String Theory

TL;DR

This paper analyzes divergences in discrete state amplitudes in 2D string theory, deriving an effective Lagrangian that encapsulates renormalized amplitudes and exploring its algebraic structure.

Contribution

It introduces a novel effective Lagrangian for discrete states in 2D string theory and connects it with homotopy Lie algebra, providing new insights into amplitude renormalization.

Findings

Pole divergences are extracted and interpreted as renormalized amplitudes.

An effective Lagrangian generating these amplitudes is constructed.

Ward identities and algebraic relations are discussed.

Abstract

Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are extracted and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian generating renormalized amplitudes for open string is written and corresponding Ward identities are presented. A relation of this Lagrangian with homotopy Lie algebra is discussed.