String theory in target space

TL;DR

This work reconsiders string theory from a target-space, on-shell perspective, showing that the tree-level S-matrix can be constructed from a compact set of principles: unitarity, locality, (super-)Poincaré invariance, universal open-string monodromy relations, and generalized BCFW-type shifts. By deriving residues at kinematic poles from monodromy relations and employing on-shell recursion, the authors reproduce known amplitudes (e.g., Veneziano/Koba-Nielsen and open superstring five-point results) and reveal the role of roots in determining amplitude structure. They systematicSum over the string spectrum using SO(D−1) irreps via projector techniques to check unitarity and re-derive no-ghost dimension/intercept constraints, demonstrating that the target-space framework can recover the usual worldsheet results and provide a pathway to general backgrounds. The paper culminates in a target-space definition of the open-string S-matrix in flat space, with steps to extend to higher points and closed strings (via KLT), while noting open questions about minimality and possible curved-background generalizations. Overall, the work offers a coherent, worldsheet-free route to string amplitudes, linking monodromy, field-theory limits, and unitarity in a unified target-space program.

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.