### 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 / J^{2} 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.

Original language | English (US) |
---|---|

Pages (from-to) | 31-52 |

Number of pages | 22 |

Journal | Annals of Physics |

Volume | 301 |

Issue number | 1 |

DOIs | |

State | Published - Oct 10 2002 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*301*(1), 31-52. https://doi.org/10.1006/aphy.2002.6293

}

*Annals of Physics*, vol. 301, no. 1, pp. 31-52. https://doi.org/10.1006/aphy.2002.6293

**Operators with large R-charge in N=4 Yang-Mills theory.** / Gross, David J.; Mikhailov, Andrei; Roiban, Radu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Operators with large R-charge in N=4 Yang-Mills theory

AU - Gross, David J.

AU - Mikhailov, Andrei

AU - Roiban, Radu

PY - 2002/10/10

Y1 - 2002/10/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037057349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037057349&partnerID=8YFLogxK

U2 - 10.1006/aphy.2002.6293

DO - 10.1006/aphy.2002.6293

M3 - Article

AN - SCOPUS:0037057349

VL - 301

SP - 31

EP - 52

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 1

ER -