Highly Excited Strings I: Generating Function

TL;DR

This paper develops a generating function for string amplitudes involving highly excited strings, extending previous theorems to more general compactifications and vertex operators, with implications for quantum gravity and string phenomenology.

Contribution

It introduces a novel approach to construct generating functions for HES string amplitudes without relying on reverse engineering, applicable to general toroidal compactifications.

Findings

Generalizes the chiral splitting theorem to HES amplitudes

Provides a new method avoiding ambiguity in loop momentum extraction

Discusses implications for quantum gravity, black holes, and cosmic superstrings

Abstract

This is the first of a series of detailed papers on string amplitudes with highly excited strings (HES). In the present paper we construct a generating function for string amplitudes with generic HES vertex operators using a fixed-loop momentum formalism. We generalise the proof of the chiral splitting theorem of D'Hoker and Phong to string amplitudes with arbitrary HES vertex operators (with generic KK and winding charges, polarisation tensors and oscillators) in general toroidal compactifications $\mathcal{E}=\mathbb{R}^{D-1,1}\times \mathbb{T}^{D_{\rm cr}-D}$ (with generic constant K\"ahler and complex structure target space moduli, background Kaluza-Klein (KK) gauge fields and torsion). We adopt a novel approach that does not rely on a "reverse engineering" method to make explicit the loop momenta, thus avoiding a certain ambiguity pointed out in a recent paper by Sen, while also keeping the genus of the worldsheet generic. This approach will also be useful in discussions of quantum gravity and in particular in relation to black holes in string theory, non-locality and breakdown of local effective field theory, as well as in discussions of cosmic superstrings and their phenomenological relevance. We also discuss the manifestation of wave/particle (or rather wave/string) duality in string theory.