Operators with Large R-Charge in N=4 Yang-Mills Theory

By D. Gross, A. Mikhailov, R. Roiban. 2002

209 citations recorded by the source corpus.

Abstract It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang–Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong–weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well-defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang–Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang–Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two-loop level that the anomalous dimension has a finite limit when the R-charge J→∞ keeps λ/J2 finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang–Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a1219421fc97fa43eef5ba9c3a64ecd744fa852b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. N. Beisert
2. A. Tseytlin
3. S. Frolov
4. M. Staudacher
5. K. Zarembo
6. R. Roiban
7. G. Arutyunov
8. D. Serban

In Nuclear and High Energy Physics

1. N. Beisert
2. M. Staudacher
3. S. Frolov
4. A. Tseytlin
5. K. Zarembo
6. G. Arutyunov
7. R. Roiban
8. Romuald A. Janik

Citations in the corpus

• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory (2003, background): “With the advent of the BMN correspondence [5] the attention has been shifted away from lower dimensional operators to operators with a large number of fields [33, 34, 35, 36, 37].”
• Transcendentality and crossing (2006, background): “However, it cannot be translated directly into anomalous dimensions of local operators as suggested in [2, 55].”
• Superstring interactions in a pp -wave background (2002, background): “[ 4 ]). It has recently been proposed [5-7] to extend this duality to include string interactions.”
• Stringing Spins and Spinning Strings (2003, background): “The result for this particular [J, 0, J ] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation.”
• On three-point correlation functions in the gauge/gravity duality (2010, methodology): “Then, the contribution of the j-th magnon to the anomalous dimension of the operator OA is given by [4, 7, 44–46] γj(g) = √ 1 + 16g2 sin pj 2 − 1 .”
• The su(2|3) dynamic spin chain (2003, methodology): “to N = 4 SYM we should use some scaling dimension that is known to all orders in perturbation theory. Namely in the planar BMN limit [3] precise all-orders results for gauge theory have been obtained [20]. In fact it is sufficient to use the scaling behaviour for BMN states, their energies should depe”
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, background): “There are some indications that this all-loop prediction for gauge theory might indeed be true [25, 109].”
• More comments on superstring interactions in the pp-wave background (2002, unknown): “J2 . Moreover the finite quantity � −J turns out to be a function of �′ and g2 2 [3, 12 , 13].”
• PP-wave string interactions from perturbative Yang-Mills theory (2002, background): “Recently, the authors of [11] have demonstrated that f2(0) = f2(∞), and have presented arguments which suggest that the planar components of fm(x) are constant functions for all m.”