### Abstract

Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N = 4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SO_{q} (6) as a deformation of the SO (6) R-symmetry structure of N = 4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N = 4 SYM. We also show that the natural context for these questions can be better phrased in terms of multi-matrix quantum mechanics rather than in four-dimensional field theories.

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

Pages (from-to) | 49-85 |

Number of pages | 37 |

Journal | Nuclear Physics B |

Volume | 702 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 6 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*702*(1-2), 49-85. https://doi.org/10.1016/j.nuclphysb.2004.09.005

**Deformations of N = 4 SYM and integrable spin chain models.** / Berenstein, David; Cherkis, Sergey.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 702, no. 1-2, pp. 49-85. https://doi.org/10.1016/j.nuclphysb.2004.09.005

}

TY - JOUR

T1 - Deformations of N = 4 SYM and integrable spin chain models

AU - Berenstein, David

AU - Cherkis, Sergey

PY - 2004/12/6

Y1 - 2004/12/6

N2 - Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N = 4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SOq (6) as a deformation of the SO (6) R-symmetry structure of N = 4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N = 4 SYM. We also show that the natural context for these questions can be better phrased in terms of multi-matrix quantum mechanics rather than in four-dimensional field theories.

AB - Beginning with the planar limit of N = 4 SYM theory, we study planar diagrams for field theory deformations of N = 4 which are marginal at the free field theory level. We show that the requirement of integrability of the full one-loop dilatation operator in the scalar sector, places very strong constraints on the field theory, so that the only soluble models correspond essentially to orbifolds of N = 4 SYM. For these, the associated spin chain model gets twisted boundary conditions that depend on the length of the chain, but which are still integrable. We also show that theories with integrable subsectors appear quite generically, and it is possible to engineer integrable subsectors to have some specific symmetry, however these do not generally lead to full integrability. We also try to construct a theory whose spin chain has quantum group symmetry SOq (6) as a deformation of the SO (6) R-symmetry structure of N = 4 SYM. We show that it is not possible to obtain a spin chain with that symmetry from deformations of the scalar potential of N = 4 SYM. We also show that the natural context for these questions can be better phrased in terms of multi-matrix quantum mechanics rather than in four-dimensional field theories.

UR - http://www.scopus.com/inward/record.url?scp=9144227085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=9144227085&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2004.09.005

DO - 10.1016/j.nuclphysb.2004.09.005

M3 - Article

AN - SCOPUS:9144227085

VL - 702

SP - 49

EP - 85

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -