Novel explicit multi spin string solitons in AdS5

Abstract

We find new explicit solutions describing closed strings spinning with equal angular momentum in two independent planes in AdS 5 . These are 2N -folded strings in the radial direction and also winding M times around an angular direction. Thus in spacetime they consist of 2N segments. Solutions fulfilling the closed string periodicity conditions exist provided N/M > 2, i.e. the strings must be folded at least six times in the radial coordinate. The strings are spinning, or actually orbiting, similarly to solutions found previously in black hole spacetimes, but unlike the one-spin solutions in AdS which spin around their center. For long strings we recover the logaritmic scaling relation between energy and spin known from the one-spin case, but different from other known two-spin cases.2

Review of AdS/CFT Integrability, Chapter II.1: Classical AdS 5 × S 5 String Solutions

“…One may also find similar rigid string solutions with ln S scaling of E − S at large spin with two non-zero spins S 1 , S 2 , i.e. moving in the whole AdS 5 [16,42,54,55,43] subject to the rigid string ansatz (3.24), i.e. t = κτ, ρ = ρ(σ), θ = θ(σ), φ 1 = ω 1 τ, φ 2 = ω 2 τ .…”

LOGARITHMIC CORRECTION TO SCALING FOR MULTISPIN STRINGS IN THE AdS5 BLACK HOLE BACKGROUND

“…Then the integrals (27)-(30) reduce to the results obtained in [18], as they should. Now introduce the dimensionless constants…”

“…Then we have also the 2 integers n and m. Notice that n and m may be constrained since k, c 0 and ω must be real. For instance, for M = 0 we find that n/m > 2 [18]. The conserved energy is given by…”

“…Many papers take therefore only the time coordinate, and the corresponding conserved energy, from AdS 5 and up to three angular momenta in S 5 , while others take only a single spin in AdS 5 . There have only been few papers with explicit examples of multi-spin strings in the AdS 5 part of the background [16,17,18]. In one of them, a generalization of the string leading to equation (1) was obtained [18].…”

“…There have only been few papers with explicit examples of multi-spin strings in the AdS 5 part of the background [16,17,18]. In one of them, a generalization of the string leading to equation (1) was obtained [18]. Namely, a two-spin string with two equal angular momenta in two independent planes of AdS 5 , leading to the result…”