The omega-infinity limit of single spikes

Abstract

A new infinite-size limit of strings in R × S 2 is presented. The limit is obtained from single spike strings by letting the angular velocity parameter ω become infinite. We derive the energy-momenta relation of ω = ∞ single spikes as their linear velocity v → 1 and their angular momentum J → 1. Generally, the v → 1, J → 1 limit of single spikes is singular and has to be excluded from the spectrum and be studied separately. We discover that the dispersion relation of omega-infinity single spikes contains logarithms in the limit J → 1. This result is somewhat surprising, since the logarithmic behavior in the string spectra is typically associated with their motion in non-compact spaces such as AdS. Omega-infinity single spikes seem to completely cover the surface of the 2-sphere they occupy, so that they may essentially be viewed as some sort of "brany strings". A proof of the sphere-filling property of omega-infinity single spikes is given in the appendix. *