The Veneziano Amplitude via Mostly BRST Exact Operator

TL;DR

This paper demonstrates that a mostly BRST exact operator can be used to fix the $PSL(2, ext{R})$ symmetry in string theory, reproducing the Veneziano amplitude and suggesting a new gauge fixing method for general amplitudes.

Contribution

It introduces a novel use of a mostly BRST exact operator to fix gauge symmetry in string amplitudes, extending its application beyond two-point functions.

Findings

Veneziano amplitude derived from a five-point function with a gauge fixing operator.

The sign factor in the amplitude is interpreted as a signed intersection number.

Conjecture of a general expression for n-point tree amplitudes with this gauge fixing operator.

Abstract

The Veneziano amplitude is derived from fixing one degree of freedom of $PSL(2,\mathbb{R})$ symmetry by the insertion of a mostly BRST exact operator. Evaluating the five-point function which consists of four open string tachyons and this gauge fixing operator, we find it equals the Veneziano amplitude up to a sign factor. The sign factor is interpreted as a signed intersection number.The result implies that the mostly BRST exact operator, which is originally used to provide two-point string amplitudes, correctly fixes the $PSL(2,\mathbb{R})$ gauge symmetry for general amplitudes. We conjecture an expression for general $n$-point tree amplitudes with an insertion of this gauge fixing operator.