Resummation of semiclassical short folded string

TY - JOUR

T1 - Resummation of semiclassical short folded string

AU - Beccaria, M.

AU - Macorini, Guido

PY - 2012/2/1

Y1 - 2012/2/1

N2 - We reconsider semiclassical quantization of folded string spinning in AdS 3 part of AdS 5 × S 5 using integrability-based (algebraic curve) method. We focus on the "short string" (small spin S) limit with the angular momentum J in S 5 scaled down according to J = ρ√S in terms of the variables J = J/√λ, S = S/√λ. The semiclassical string energy in this particular scaling limit admits P the double expansion E =Σ = n=0 ∞ Σ p=0 ∞ (√λ) 1-n a n,p(ρ) S p+1/2. It behaves smoothly as J → 0 and partially resums recent results by Gromov and Valatka. We explicitly compute various one-loop coefficients a 1,p(ρ) by summing over the fluctuation frequencies for integrable perturbations around the classical solution. For the simple folded string, the result agrees with what could be derived exploiting a recent conjecture of Basso. However, the method can be extended to more general situations. As an example, we consider the m-folded string where Basso's conjecture fails. For this classical solution, we present the exact values of a 1,0(ρ) and a 1,1(ρ) for m = 2, 3, 4, 5 and explain how to work out the general case.

AB - We reconsider semiclassical quantization of folded string spinning in AdS 3 part of AdS 5 × S 5 using integrability-based (algebraic curve) method. We focus on the "short string" (small spin S) limit with the angular momentum J in S 5 scaled down according to J = ρ√S in terms of the variables J = J/√λ, S = S/√λ. The semiclassical string energy in this particular scaling limit admits P the double expansion E =Σ = n=0 ∞ Σ p=0 ∞ (√λ) 1-n a n,p(ρ) S p+1/2. It behaves smoothly as J → 0 and partially resums recent results by Gromov and Valatka. We explicitly compute various one-loop coefficients a 1,p(ρ) by summing over the fluctuation frequencies for integrable perturbations around the classical solution. For the simple folded string, the result agrees with what could be derived exploiting a recent conjecture of Basso. However, the method can be extended to more general situations. As an example, we consider the m-folded string where Basso's conjecture fails. For this classical solution, we present the exact values of a 1,0(ρ) and a 1,1(ρ) for m = 2, 3, 4, 5 and explain how to work out the general case.

U2 - 10.1007/jhep02(2012)092

DO - 10.1007/jhep02(2012)092

M3 - Journal article

SN - 1126-6708

VL - 2012

SP - 092

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 2

ER -