String theory in target space

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.

66 pages, many figures

References in corpus (12)

• New Relations for Gauge-Theory Amplitudes
• The Pomeron and Gauge/String Duality
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Consistency Conditions on the S-Matrix of Massless Particles
• On BCFW shifts of integrands and integrals
• On-shell Recursion in String Theory
• New Relations for Gauge-Theory Amplitudes with Matter
• The covariant perturbative string spectrum
• Higher Spin Scattering in Superstring Theory
• α'-Expansion of Open String Disk Integrals via Mellin Transformations

Cited by in corpus (11)

• The EFT-Hedron
• More on Soft Theorems: Trees, Loops and Strings
• Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude
• Conformal correlators of mixed-symmetry tensors
• Carving out the Space of Open-String S-matrix
• Generalizations of the Double-Copy: the KLT Bootstrap
• Classical Limit of Higher-Spin String Amplitudes
• The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop
• On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
• Positivity of the Hypergeometric Coon Amplitude
• A Note on S-Matrix Bootstrap for Amplitudes with Linear Spectrum