Reduction of Open String Amplitudes by Mostly BRST Exact Operators

TL;DR

This paper presents a method to simplify open string tree-level amplitudes by using mostly BRST exact operators for gauge fixing, focusing on tachyon states, and analyzing the resulting correlation functions and moduli integrals.

Contribution

It introduces a novel approach to reduce open string amplitudes using mostly BRST exact operators, providing new insights into amplitude calculations and sign ambiguities.

Findings

Two-point tachyon amplitude derived from three-point function

Three-point tachyon amplitude derived from four-point function

Discussion of sign ambiguities in amplitude calculations

Abstract

We study two and three-point tree-level amplitudes of open strings. These amplitudes are reduced from higher-point correlation functions by using mostly BRST exact operators for gauge fixing. For simplicity, we focus on an open string tachyon. The two-point amplitude of open string tachyons is reduced from a three-point function of two tachyon vertex operators and one mostly BRST exact operator. Similarly the three-point amplitude is from a four-point function of three tachyon vertex operators and one mostly BRST exact operator. One can also obtain the two-point amplitude from the four-point function of two tachyon vertex operators and two mostly BRST exact operators. In these derivation from four-point functions, moduli integrals are significant. We discuss the overall signs of amplitudes which are indefinite in this formalism.