Abstract
It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are (generalised) Britto-Cachazo-Feng-Witten shifts, as well as the monodromy relations for open string theory and the Kawai-Lewellen-Tye relations for closed string theory. The roots of the scattering amplitudes and especially their appearance in the residues at the kinematic poles are central to the story. These residues determine the amplitudes through on-shell recursion relations. Several checks of the formalism are presented, including a computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore the question of target space unitarity is (re-)investigated. For the Veneziano amplitude this question is reduced by Poincare invariance, unitarity and locality to that of positivity of a particular numerical sum. Interestingly, this analysis produces the main conditions of the no-ghost theorem on dimension and intercept from the first three poles of this amplitude.
Highlights
The birth of string theory is usually taken to be the publication of Veneziano’s paper [1]
It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description
Proving on-shell recursion relations for a specific field theory involves a study of the behaviour of a scattering amplitude when the momenta of two of the legs tend to infinity in a particular way
Summary
The birth of string theory is usually taken to be the publication of Veneziano’s paper [1]. Proving on-shell recursion relations for a specific field theory involves a study of the behaviour of a scattering amplitude when the momenta of two of the legs tend to infinity in a particular way. It will be shown that the monodromy relations can be used to predict the location of the roots of the residues at kinematic poles but even that with some additional work they fix the residue of at least the Koba-Nielsen amplitudes completely. By on-shell recursion this provides the complete scattering amplitudes in the string theory It is an interesting question how results which are usually derived through the worldsheet picture find a place in a target space approach.
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