High energy scattering and null strings

Abstract: We propose an instrinsic worldsheet description of the ultra-high energy regime of string scattering based on worldsheet symmetries. At very high energies, the fundamental string becomes tensionless and in flat target spacetimes, the worldsheet becomes a null surface. Tensionless null strings thus emerge and the worldsheet symmetries morph from two copies of the Virasoro algebra to the two dimensional (2d) conformal Carroll or equivalently the 3d Bondi-van der Burgh-Metzner-Sachs (BMS) algebra. Tensionless strings have three inequivalent vacua over which they can be constructed, leading to distinct quantum theories. High energy tensile strings naturally connect to null strings built on the so-called induced vacuum. Our principle goal in this paper is the construction of scattering amplitudes for null strings in the induced vacuum. We show that these amplitudes, constructed from worldsheet methods of the null string, coincide with the high energy limit of usual string amplitudes. A crucial part of our analysis is the construction of integrated vertex operators. This achieved by relying on lessons from the parent string theory and following the tensionless limit carefully. A striking feature of the null string is the blurring of differences between open and closed strings. We see this at the level of the amplitudes as well. We then focus on four-point amplitudes and recover all expected regimes including the Gross-Mende regime and the Regge limit. We finally comment on a new class of vertex operators which arise naturally only in the zero tension string. This reproduces all our earlier analyses when put onshell but also has hints of signatures beyond the perturbative tensile string.