Longitudinal nonlocality in the string S-matrix

Abstract

We analyze four and five-point tree-level open string S-matrix amplitudes in the Regge limit, exhibiting some basic features which indicate longitudinal nonlocality, as suggested by light cone gauge calculations of string spreading. Using wavepackets to localize the asymptotic states, we compute the peak trajectories followed by the incoming and outgoing strings, determined by the phases in the amplitudes. These trajectories trace back in all dimensions such that the incoming strings deflect directly into corresponding outgoing ones, as expected from a Reggeon analysis. Bremsstrahlung radiation at five points emerges from the deflection point, corroborating this picture. An explicit solution for the intermediate state produced at four points in the $s$-channel exists, with endpoints precisely following the corresponding geometry and a periodicity which matches the series of time delays predicted by the amplitude. We find a nonzero peak impact parameter for this process, and show that it admits an interpretation in terms of longitudinal-spreading induced string joining, at the scale expected from light cone calculations, and does not appear to admit a straightforward interpretation purely in terms of the well-established transverse spreading. At five points, we exhibit a regime with advanced emission of one of the deflected outgoing strings. This strongly suggests early interaction induced by longitudinal nonlocality. In a companion paper, we apply string spreading to horizon dynamics.

40 pages, 10 figures. v2: typos fixed

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• The Pomeron and Gauge/String Duality
• Space/Time Non-Commutativity and Causality
• Black Hole Complementarity vs. Locality
• Strings, Black Holes and Lorentz Contraction
• Gravitational effects in ultrahigh-energy string scattering
• Finite momentum at string endpoints
• String-theoretic breakdown of effective field theory near black hole horizons
• Backdraft: String Creation in an Old Schwarzschild Black Hole
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• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
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• String-theoretic breakdown of effective field theory near black hole horizons
• The long string at the stretched horizon and the entropy of large non-extremal black holes
• Stringy Horizons and UV/IR Mixing
• Highly Excited Strings I: Generating Function
• Revisiting noninteracting string partition functions in Rindler space
• The quantum cat map on the modular discretization of extremal black hole horizons
• Varying dilaton as a tracer of classical string interactions
• Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers