Consistent Off-Shell Tree String Amplitudes

TL;DR

This paper presents a method for constructing off-shell tree-level bosonic string amplitudes using operator formalism, ensuring projective invariance and reproducing known gauge theory results in the low-energy limit.

Contribution

It introduces a novel operator-based construction for off-shell string amplitudes that maintains projective invariance and matches gauge theory amplitudes at low energy.

Findings

Constructed off-shell tree amplitudes for open and closed bosonic strings.

Ensured projective invariance in the amplitude construction.

Reproduced the three-gluon amplitude in the low-energy limit.

Abstract

We give a construction of off-shell tree bosonic string amplitudes, based on the operatorial formalism of the $N$-string Vertex, with three external massless states both for open and closed strings by requiring their being projective invariant. In particular our prescription leads, in the low-energy limit, to the three-gluon amplitude in the usual covariant gauge.