Leading quantum correction to energy of ‘short’ spiky strings

Macorini²

2012

J. High Energ. Phys.

Self Cite

We reconsider semiclassical quantization of folded string spinning in AdS_3 part of AdS_5 X 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 \cal J = rho \sqrt \cal S in terms of the variables \cal J = J/\sqrt\lambda, \cal S = S/\sqrt\lambda. The semiclassical string energy in this particular scaling limit admits the double expansion E = \sum_{n=0}^{\infty}\sum_{p=0}^{\infty} (\sqrt\lambda)^{1-n}\,a_{n,p}(rho)\, \cal 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}(rho) 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}(rho) and a_{1,1}(rho) for m=2, 3, 4, 5 and explain how to work out the general case.Comment: 19 page

“…As a final check, we remark that the values Ñ ½ ¼ ´¼µ agree with a general analysis of the short Ñ-folded string in the fixed Â Ë regime [20] as they should.…”

Section: Resummed Values At â ¼ It Is Interesting To Compute the Valu...supporting

confidence: 79%

Resummation of semiclassical short folded string

Macorini²

2012

J. High Energ. Phys.

Self Cite

“…34 As we have checked explicitly from the results in Appendix of [30], the same subleading 1/J 2 finite-size term as in (A.6) appears also for the circular (S, J) string state in the sl(2) sector (here J is the momentum along the circle in S 5 which the string is wound on). This suggests the universality of the terms given explicitly in (A.6) in the sl(2) sector.…”

Section: Circular String With Spins S = Jmentioning

confidence: 59%

“Short” spinning strings and structure of quantumAdS5×S5spectrum

Giombi

Macorini³

et al. 2012

Phys. Rev. D

Using information from the marginality conditions of vertex operators for the AdS 5 ×S 5 superstring, we determine the structure of the dependence of the energy of quantum string states on their conserved charges and the string tension ∼ √ λ. We consider states on the leading Regge trajectory in the flat space limit which carry one or two (equal) spins in AdS 5 or S 5 and an orbital momentum in S 5 , with Konishi multiplet states being particular cases. We argue that the coefficients in the energy may be found by using a semiclassical expansion. By analyzing the examples of folded spinning strings in AdS 5 and S 5 as well as three cases of circular two-spin strings we demonstrate the universality of transcendental (zeta-function) parts of few leading coefficients. We also show the consistency with target space supersymmetry with different states belonging to the same multiplet having the same non-trivial part of the energy. We suggest, in particular, that a rational coefficient (found by Basso for the folded string using Bethe Ansatz considerations and which, in general, is yet to be determined by a direct two-loop string calculation) should, in fact, be universal.

“…The relevant string polarizations can be assigned at the two sheets A, B of the disconnected AdS 3 algebraic curve (see for instance [20]) according to the following table where we adopt the AdS 5 × S 5 labeling of off-shell frequencies of [40] polarization sheet(s) off-shell frequency ( 2, 3)…”

Section: Algebraic Curve One-loop Quantization and Comparison With Womentioning

confidence: 99%

Quantum corrections to short folded superstring in AdS 3 × S 3 × M 4

Macorini²

2013

J. High Energ. Phys.

We consider integrable superstring theory on AdS 3 × S 3 × M 4 where M 4 = T 4 or M 4 = S 3 × S 1 with generic ratio of the radii of the two 3-spheres. We compute the oneloop energy of a short folded string spinning in AdS 3 and rotating in S 3 . The computation is performed by world-sheet small spin perturbation theory as well as by quantizing the classical algebraic curve characterizing the finite-gap equations. The two methods give equal results up to regularization contributions that are under control. One important byproduct of the calculation is the part of the energy which is due to the dressing phase in the Bethe Ansatz. Remarkably, this contribution E dressing 1 turns out to be independent on the radii ratio. In the M 4 = T 4 limit, we discuss how E dressing 1 relates to a recent proposal for the dressing phase tested in the su(2) sector. We point out some difficulties suggesting that quantization of the AdS 3 classical finite-gap equations could be subtler than the easier AdS 5 × S 5 case.