Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

By Z. Bajnok, Romuald A. Janik. 2008

290 citations recorded by the source corpus.

We derive the perturbative four loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Luscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1c3ca40108bed13c9af6276a1971ee61698a6865

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Citations in the corpus

Extended Y-system for the AdS5/CFT4 correspondence (2010, background): “A first important step leading to the partial solution of this problem was made by Bajnok and Janik in [14].”
Foundations of the AdS5 × S5 superstring: I (2009, methodology): “The corresponding computation has been done [46] for the simplest case of the so-called Konishi operator and stunning agreement with a very complicated four-loop result based on the standard Feynman diagrammatics [47] has been found.”
Four loop twist two, BFKL, wrapping and strings (2008, methodology): “In [28] the authors conjectured a Lüscher type formula for generic multiparticle states and successfully applied it for the Konishi case: M = 2.”
String hypothesis for the AdS5 × S5 mirror (2009, methodology): “This observation was used in the derivation [37] of the four-loop scaling dimension of the Konishi operator by means of Lüscher’s formulae [38].”
T-systems and Y-systems in integrable systems (2010, background): “We do not intend to cover them here but refer to the literatures that will be cited in the next subsection and [179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192] for example and references therein.”
Wrapping at four loops in N=4 SYM theory (2007, methodology): “We have corrected a factor of 2 missing in W5 of Figure 1 after the appearance of [ 28 ].”
Integrable Wilson loops (2012, methodology): “Within the context of integrability of N = 4 SYM the double row transfer matrix was studied in [54, 55] and used in calculating finite size corrections to the spectrum of insertions into determinant operators (giant gravitons in the dual string theory) in [56, 57], generalizing the pioneering work o”
Five loop Konishi from AdS/CFT (2009, methodology): “The formalism of the leading multiparticle Lüscher corrections have been quantitatively tested in the case of the 4-loop anomalous dimension of the Konishi operator where the leading order wrapping diagrams have been calculated perturbatively [37, 38].”
Towards integrability for AdS 3 / CFT 2 ?> (2014, methodology): “As for wrapping effects, it was shown [109] that the approach of Lüscher [71, 72] can be extended to the AdS5 × S(5) NLSM, and in fact that the whole mirror TBA approach can be applied, yielding an exact description of the spectrum.”
Five-loop anomalous dimension of twist-two operators (2009, methodology): “In the seminal paper [19] it was proposed to evaluate the Lüscher corrections, previously proposed for the AdS5 × S 5 sigma model in [20], to calculate the leading wrapping corrections to the simplest unprotected operator in the sl(2) sector, the Konishi operator.”
N = 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations (2008, methodology): “The result can be compared with various semi-classical string calculations [27] as has been done for the AdS5/CFT4 in [28] and with perturbative CS computations along the line of [20].”
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, background): “It comes along with the ‘mirror’ Smatrix S(u, v) that is a physical object on its own; it yields for instance the Casimir energy of the Integrable system in finite volume through the so-called Lüscher formula [61, 62].”
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model (2009, unknown): “4) Here the sl(2) S-matrix S ′ sl(2) in the uniform light-cone gauge [1] with the gauge parameter a = 0 can be written in the form [53, 54, 5, 16] S ′ sl(2)(u, u ′) = S ′ (u − u′)−1 ΣQQ′(u, u′)−2 , (2.”