### Abstract

We consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_{5} × S^{5} by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters γ_{i} which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N = 4 SYM theory, but with scalar and Yukawa interactions "deformed" by γ_{i}-dependent phases. The special case of equal γ_{i} = γ corresponds to the N = 1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal γ_{i} this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective "Landau-Lifshitz" actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e., it allows one to capture the right vacuum states and the "macroscopic spin wave" sector of states of the spin chain in the continuum coherent state effective action.

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

Pages (from-to) | 1-44 |

Number of pages | 44 |

Journal | Nuclear Physics B |

Volume | 731 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 19 2005 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*731*(1-2), 1-44. https://doi.org/10.1016/j.nuclphysb.2005.10.004

}

*Nuclear Physics B*, vol. 731, no. 1-2, pp. 1-44. https://doi.org/10.1016/j.nuclphysb.2005.10.004

**Gauge-string duality for (non)supersymmetric deformations of N = 4 super-Yang-Mills theory.** / Frolov, S. A.; Roiban, R.; Tseytlin, A. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gauge-string duality for (non)supersymmetric deformations of N = 4 super-Yang-Mills theory

AU - Frolov, S. A.

AU - Roiban, R.

AU - Tseytlin, A. A.

PY - 2005/12/19

Y1 - 2005/12/19

N2 - We consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS5 × S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters γi which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N = 4 SYM theory, but with scalar and Yukawa interactions "deformed" by γi-dependent phases. The special case of equal γi = γ corresponds to the N = 1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal γi this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective "Landau-Lifshitz" actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e., it allows one to capture the right vacuum states and the "macroscopic spin wave" sector of states of the spin chain in the continuum coherent state effective action.

AB - We consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS5 × S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters γi which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N = 4 SYM theory, but with scalar and Yukawa interactions "deformed" by γi-dependent phases. The special case of equal γi = γ corresponds to the N = 1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal γi this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective "Landau-Lifshitz" actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e., it allows one to capture the right vacuum states and the "macroscopic spin wave" sector of states of the spin chain in the continuum coherent state effective action.

UR - http://www.scopus.com/inward/record.url?scp=27744507581&partnerID=8YFLogxK

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U2 - 10.1016/j.nuclphysb.2005.10.004

DO - 10.1016/j.nuclphysb.2005.10.004

M3 - Article

AN - SCOPUS:27744507581

VL - 731

SP - 1

EP - 44

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -