Logarithmic scaling in gauge/string correspondence
By A. Belitsky, A. Gorsky, G. Korchemsky. 2006
175 citations recorded by the source corpus.
Abstract We study anomalous dimensions of (super)conformal Wilson operators at weak and strong coupling making use of the integrability symmetry on both sides of the gauge/string correspondence and elucidate the origin of their single-logarithmic behavior for long operators/strings in the limit of large Lorentz spin. On the gauge theory side, we apply the method of the Baxter Q -operator to identify different scaling regimes in the anomalous dimensions in integrable sectors of (supersymmetric) Yang–Mills theory to one-loop order and determine the values of the Lorentz spin at which the logarithmic scaling sets in. We demonstrate that the conventional semiclassical approach based on the analysis of the distribution of Bethe roots breaks down in this domain. We work out an asymptotic expression for the anomalous dimensions which is valid throughout the entire region of variation of the Lorentz spin. On the string theory side, the logarithmic scaling occurs when two most distant points of the folded spinning string approach the boundary of the AdS space. In terms of the spectral curve for the classical string sigma model, the same configuration is described by an elliptic curve with two branching points approaching values determined by the square root of the 't Hooft coupling constant. As a result, the anomalous dimensions cease to obey the BMN scaling and scale logarithmically with the Lorentz spin.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/c5a16bc7e81ce830ac96b681a99c133e4bae02d5
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Citations in the corpus
- Semiclassical quantization of spinning strings in AdS4 × ℂℙ3 (2008, background): “where the function f(λ) is the universal scaling function, also known as the cusp anomaly [20, 21].”
- An operator product expansion for polygonal null Wilson loops (2010, methodology): “However, we need to add the anomalous dimension per excitation δ∆ Lλ = 3 of the state tr ( F+i )L [24] to the result of [23].”
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- Transcendentality and crossing (2006, background): “e twist-L is a universal function of the coupling constant g. This suggests that it should coincide with the scaling function of twist-two operators. For a similar discussion, albeit at one loop, see [27]. Despite the similarity to a thermodynamic limit, the computation is quite subtle due to the si”
- Integrability and transcendentality (2006, background): “For a very recent discussion of this point, on the one-loop level, see [27].”
- Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, unknown): “The relevant analysis was carried out in [14] (see also [15] and [16]) building on previous studies [17, 18].”
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