Abstract
We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.
Highlights
Semiclassical spectra of worldsheet theory in various curved spacetimes have been studied since seminal works by de Vega and Sanchez in 80’s [9, 10] and the followups [11–13]
We studied a class of semiclassical strings in de Sitter space and the corresponding Regge trajectories
We showed for folded strings that there exist the maximum spin and energy in each Regge trajectory for a fixed internal charge and a fixed folding number
Summary
In this paper we study string Regge trajectories on dS3 × S1 (which may be identified with an appropriate subspace of a larger target space). To utilize results in AdS, it is convenient to introduce a coordinate ρ defined by sin ρ = r (0 ≤ ρ ≤ π/2), in terms of which the metric reads ds2 = R2 − cos2ρ dt2 + dρ2 + sin[2] ρ dφ[2 ]. Note that in these coordinates, the observer sitting at the origin and the cosmological horizon are located at ρ = 0 and ρ = π/2, respectively. We absorb the radius of the circle S1 into the definition of φ
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