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 longitudinalspreading 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.

Long-range nonlocality in six-point string scattering: Simulation of black hole infallers

“…Light cone [1] and saddle point [2] calculations strongly suggest a significant degree of longitudinal nonlocality in string theory in the regime of large center of mass energy compared to the string scale, E 1/ √ α . As reviewed in [3,4], both analyses [1,2] lead to the relations 1…”

“…This has been discussed in a number of very interesting works such as [7][8] [9] [10], but the results on the basic question of longrange interaction were inconclusive. In [4], we began a detailed analysis of this using wavepackets convolved against four and five point tree-level string scattering amplitudes, exhibiting features -such as the deflection of the traced-back trajectory of a scattered string wavepacket before its center of mass would collide -which are difficult to explain purely by the transverse spreading (∆X ⊥ ) 2 . Excluding purely transverse non-locality is important, and the arguments in [4] are subtle, giving only indirect indications of the long range E/k 2 ⊥ ≤ α E predicted by (1.1).…”

“…In [4], we began a detailed analysis of this using wavepackets convolved against four and five point tree-level string scattering amplitudes, exhibiting features -such as the deflection of the traced-back trajectory of a scattered string wavepacket before its center of mass would collide -which are difficult to explain purely by the transverse spreading (∆X ⊥ ) 2 . Excluding purely transverse non-locality is important, and the arguments in [4] are subtle, giving only indirect indications of the long range E/k 2 ⊥ ≤ α E predicted by (1.1). More generally, it is crucial to take into account the possibility that fluctuations in the central positions of strings could account for effects that would otherwise be ascribed to the longitudinal spreading.…”

Revisiting noninteracting string partition functions in Rindler space

“…Indeed, setting s = πα τ 2 and dropping the temperature-independent parts, one finds agreement with (37). Equation (38) was written down by Emparan 20 years ago [2]. The main difference is that in the case at hand, the computation is much better motivated and it is clear that Emparan computed the non-interacting free energy, obtained by neglecting all spin-dependent parts of the heat kernels and treating every higher spin field as a scalar.…”

“…1 The cigar theory was further studied recently in [32] [33] [34] [35]. In [36][37] [38], real-time aspects of strings near horizons were discussed (non-adiabatic string production and elongation of strings falling near a black hole horizon). Long strings were also argued to be very important in between both horizons of rotating black holes in [39] [40].…”