Abstract
A new infinite-size limit of strings in R×S2 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.
Highlights
Introduction and motivationThe AdS/CFT correspondence has been revolutionized during the past ten years by the introduction of integrability methods [1,2] that can be used in order to solve the theories on bothM
We have mostly described what happens in the su (2) sector, one may generalize this discussion to the entire AdS/CFT, by replacing the scalar impurity X with any of the fields Y, Fμν, Dμ, ψa,α of N = 4 super Yang–Mills (SYM), and move from R × S2 to the full AdS5 × S5 spacetime in order to get the dual picture
We find the appearance of logarithms in the dispersion relation of strings in R × S2 rather surprising
Summary
The AdS/CFT correspondence has been revolutionized during the past ten years by the introduction of integrability methods [1,2] that can be used in order to solve the theories on both. When v → 1±, single spikes have finite but still large size/winding and their dispersion relation assumes the following general form [20] (at strong coupling, λ = ∞): E−p=q + ∞ 22. The size (i.e. the energy) of single spike strings is large/infinite because their energy is equal to their momentum (i.e. their length/winding/angular extent) to lowest order (cf equation (1.8)) and the latter is large/infinite. The aim of the present paper is to clarify the above situation by computing the dispersion relation of classical single spikes in the infinite-size/winding limit (see Fig. 2):. The structure of (1.19) for infinite size/winding single spikes is highly reminiscent of the large-spin expansions of the anomalous dimensions of twist-2 operators and those of Gubser–Klebanov– Polyakov (GKP) strings in AdS3 [27]. We provide a proof of the space-filling property of omega-infinity single spikes
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