### Abstract

Double trace deformations, that is products of two local operators, define perturbations of conformal field theories that can be studied exactly in the large-N limit. Even when the double trace deformation is irrelevant in the infrared, it is believed to flow to an ultraviolet fixed point. In this note we define the Källen-Lehmann representation of the two-point function of a local operator O in a theory perturbed by the square of such operator. We use such representation to discover potential pathologies at intermediate points in the flow that may prevent to reach the UV fixed point. We apply the method to an “extremal” deformation that naively would flow to a UV fixed point where the operator O would saturate the unitarity bound Δ=d2−1. We find that the UV fixed point is not conformal and that the deformed two-point function propagates unphysical modes. We interpret the result as showing that the flow to the UV fixed point does not exist. This resolves a potential puzzle in the holographic interpretation of the deformation.

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

Article number | 40 |

Journal | Journal of High Energy Physics |

Volume | 2016 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2016 |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Conformal Field Theory
- Renormalization Group

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2016*(11), [40]. https://doi.org/10.1007/JHEP11(2016)040

**Notes on relevant, irrelevant, marginal and extremal double trace perturbations.** / Porrati, Massimo; Yu, Cedric C Y.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2016, no. 11, 40. https://doi.org/10.1007/JHEP11(2016)040

}

TY - JOUR

T1 - Notes on relevant, irrelevant, marginal and extremal double trace perturbations

AU - Porrati, Massimo

AU - Yu, Cedric C Y

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Double trace deformations, that is products of two local operators, define perturbations of conformal field theories that can be studied exactly in the large-N limit. Even when the double trace deformation is irrelevant in the infrared, it is believed to flow to an ultraviolet fixed point. In this note we define the Källen-Lehmann representation of the two-point function of a local operator O in a theory perturbed by the square of such operator. We use such representation to discover potential pathologies at intermediate points in the flow that may prevent to reach the UV fixed point. We apply the method to an “extremal” deformation that naively would flow to a UV fixed point where the operator O would saturate the unitarity bound Δ=d2−1. We find that the UV fixed point is not conformal and that the deformed two-point function propagates unphysical modes. We interpret the result as showing that the flow to the UV fixed point does not exist. This resolves a potential puzzle in the holographic interpretation of the deformation.

AB - Double trace deformations, that is products of two local operators, define perturbations of conformal field theories that can be studied exactly in the large-N limit. Even when the double trace deformation is irrelevant in the infrared, it is believed to flow to an ultraviolet fixed point. In this note we define the Källen-Lehmann representation of the two-point function of a local operator O in a theory perturbed by the square of such operator. We use such representation to discover potential pathologies at intermediate points in the flow that may prevent to reach the UV fixed point. We apply the method to an “extremal” deformation that naively would flow to a UV fixed point where the operator O would saturate the unitarity bound Δ=d2−1. We find that the UV fixed point is not conformal and that the deformed two-point function propagates unphysical modes. We interpret the result as showing that the flow to the UV fixed point does not exist. This resolves a potential puzzle in the holographic interpretation of the deformation.

KW - AdS-CFT Correspondence

KW - Conformal Field Theory

KW - Renormalization Group

UR - http://www.scopus.com/inward/record.url?scp=84994765447&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994765447&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2016)040

DO - 10.1007/JHEP11(2016)040

M3 - Article

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 40

ER -