A large spin limit of strings on in a non-compact sector

Sakai, Kazuhiro; Satoh, Yuji

doi:10.1016/j.physletb.2006.12.035

Cited by 15 publications

(20 citation statements)

References 34 publications

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“…. [17,18]. Similarly, they enjoy the expansion [19,10] γ(g, s, j) = f (g, j) ln s + ∞ n=0 f (n) (g, j)(ln s) −n + O ((ln s)/s) , (1.5) generating an infinite number of other scaling functions.…”

Section: General Setting Aims and Resultsmentioning

confidence: 99%

“…Similarly, they enjoy the expansion [19,10] γ(g, s, j) = f (g, j) ln s + ∞ n=0 f (n) (g, j)(ln s) −n + O ((ln s)/s) , (1.5) generating an infinite number of other scaling functions. Yet, in the aforementioned semiclassical string (world-sheet) expansion the natural parameter is not even j, but of course its scaled version [17,18,20,21]…”

Section: General Setting Aims and Resultsmentioning

confidence: 99%

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TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

Fioravanti

Rossi

2012

J. High Energ. Phys.

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We consider high spin, $s$, long twist, $L$, planar operators (asymptotic Bethe Ansatz) of strong ${\cal N}=4$ SYM. Precisely, we compute the minimal anomalous dimensions for large 't Hooft coupling $\lambda$ to the lowest order of the (string) scaling variable $\ell \sim L/ (\ln \mathcal{S} \sqrt{\lambda})$ with GKP string size $\sim\ln \mathcal{S}\equiv 2 \ln (s/\sqrt{\lambda})$. At the leading order $(\ln \mathcal{S}) \cdot \ell ^2 $, we can confirm the O(6) non-linear sigma model description for this bulk term, without boundary term $(\ln \mathcal{S})^0$. Going further, we derive, extending the O(6) regime, the exact effect of the size finiteness. In particular, we compute, at all loops, the first Casimir correction $\ell ^0/\ln \mathcal{S}$ (in terms of the infinite size O(6) NLSM), which reveals only one massless mode (out of five), as predictable once the O(6) description has been extended. Consequently, upon comparing with string theory expansion, at one loop our findings agree for large twist, while reveal for negligible twist, already at this order, the appearance of wrapping. At two loops, as well as for next loops and orders, we can produce predictions, which may guide future string computations.Comment: Version 2 with: new exact expression for the Casimir energy derived (beyond the first two loops of the previous version); UV theory formulated and analysed extensively in the Appendix C; origin of the O(6) NLSM scattering clarified; typos correct and references adde

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Section: General Setting Aims and Resultsmentioning

confidence: 99%

Section: General Setting Aims and Resultsmentioning

confidence: 99%

TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

Fioravanti

Rossi

2012

J. High Energ. Phys.

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“…The result should be of more general nature than our present discussion and may help in understanding better the AdS/CFT correspondence in the sector states represented by strings moving in AdS 5 (cf. [4,32]). …”

Section: Discussionmentioning

confidence: 99%

Spiky strings, lightlike Wilson loops, and pp-wave anomaly

Kruczenski

Tseytlin

2008

Phys. Rev. D

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We consider rigid rotating closed strings with spikes in AdS 5 dual to certain higher twist operators in N = 4 SYM theory. In the limit of large spin when the spikes reach the boundary of AdS 5 , the solutions with different numbers of spikes are related by conformal transformations, implying that their energy is determined by the same function of the 't Hooft coupling f (λ) that appears in the anomalous dimension of twist 2 operators or in the cusp anomaly. In the limit when the number of spikes goes to infinity, we find an equivalent description in terms of a string moving in an AdS pp-wave background. From the boundary theory point of view, the corresponding description is based on the gauge theory living in a 4d pp-wave space. Then, considering a charge moving at the speed of light, or a null Wilson line, we find that the integrated energy momentum tensor has a logarithmic UV divergence that we call the "pp-wave anomaly". The AdS/CFT correspondence implies that, for N = 4 SYM, this pp-wave anomaly should have the same value as the cusp anomaly. We verify this at lowest order in SYM perturbation theory. As a side result of our string theory analysis, we find new open string solutions in the Poincare patch of the standard AdS space which end on a light-like Wilson line and also in two parallel light-like Wilson lines at the boundary.

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“…To have a smooth limit J → 0 one should, however, replace ln S J by ln S in eqs.(1.2)-(1.4). Let us mention that a discussion of the logarithmic scaling at the classical string side appeared also in [16]. with x defined in (1.3).…”

Section: )mentioning

confidence: 99%

Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT

2007

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We compute 1-loop correction E 1 to the energy of folded string in AdS 5 × S 5 (carrying spin S in AdS 5 and momentum J in S 5 ) using a "long string" approximation in which S ≫ J ≫ 1. According to the AdS/CFT the function E 1 should represent first subleading correction to strong coupling expansion of anomalous dimension of higher twist SL(2) sector operators of the form TrD S Z J . We show that E 1 smoothly interpolates between the ln S regime (previously found in the J → 0 case) and the λ/J 2 ln 3 (S/J) regime (which is the leading correction to the thermodynamic limit on the spin chain side). This supports the universality of the ln S scaling. As in the previous work, we also find "nonanalytic" corrections related to non-trivial 1-loop phase in the corresponding Bethe ansatz S-matrix.

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A large spin limit of strings on in a non-compact sector

Cited by 15 publications

References 34 publications

TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT

Spiky strings, lightlike Wilson loops, and pp-wave anomaly

Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT

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