### Abstract

We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS
_{4}, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.

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

Pages (from-to) | 231-242 |

Number of pages | 12 |

Journal | Nuclear Physics B - Proceedings Supplements |

Volume | 171 |

Issue number | SPEC. ISS. |

DOIs | |

State | Published - Sep 2007 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B - Proceedings Supplements*,

*171*(SPEC. ISS.), 231-242. https://doi.org/10.1016/j.nuclphysbps.2007.06.014

**Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals.** / Elitzur, S.; Giveon, A.; Porrati, M.; Rabinovici, E.

Research output: Contribution to journal › Article

*Nuclear Physics B - Proceedings Supplements*, vol. 171, no. SPEC. ISS., pp. 231-242. https://doi.org/10.1016/j.nuclphysbps.2007.06.014

}

TY - JOUR

T1 - Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals

AU - Elitzur, S.

AU - Giveon, A.

AU - Porrati, M.

AU - Rabinovici, E.

PY - 2007/9

Y1 - 2007/9

N2 - We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS 4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.

AB - We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS 4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.

UR - http://www.scopus.com/inward/record.url?scp=34547741561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547741561&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysbps.2007.06.014

DO - 10.1016/j.nuclphysbps.2007.06.014

M3 - Article

AN - SCOPUS:34547741561

VL - 171

SP - 231

EP - 242

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - SPEC. ISS.

ER -