Resummation of semiclassical short folded string
Abstract
We reconsider semiclassical quantization of folded string spinning in AdS3 part of AdS5 × S5 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 {mathcal J} = ρ sqrt {S} in terms of the variables {mathcal J} = J/ sqrt {λ } , S = S/ sqrt {λ } . The semi-classical string energy in this particular scaling limit admits the double expansion E = {sum {_{{n = 0}}^{infty }sum {_{{p = 0}}^{infty }left( {sqrt {λ } } right)} }^{{1 - n}}}{a_{{n,p}}}left( ρ right){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 a1, 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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- February 2012
- DOI:
- 10.1007/JHEP02(2012)092
- arXiv:
- arXiv:1201.0608
- Bibcode:
- 2012JHEP...02..092B
- Keywords:
-
- AdS-CFT Correspondence;
- Integrable Field Theories;
- High Energy Physics - Theory
- E-Print:
- 19 pages