### Abstract

We consider the Wilson-Polchinski exact renormalization group (RG) applied to the generating functional of single-trace operators at a free-fixed point in d=2+1 dimensions. By exploiting the rich symmetry structure of free-field theory, we study the geometric nature of the RG equations and the associated Ward identities. The geometry, as expected, is holographic, with anti-de Sitter spacetime emerging correspondent with RG fixed points. The field theory construction gives us a particular vector bundle over the d+1-dimensional RG mapping space, called a jet bundle, whose structure group arises from the linear orthogonal bilocal transformations of the bare fields in the path integral. The sources for quadratic operators constitute a connection on this bundle and a section of its endomorphism bundle. Recasting the geometry in terms of the corresponding principal bundle, we arrive at a structure remarkably similar to the Vasiliev theory, where the horizontal part of the connection on the principal bundle is Vasiliev's higher spin connection, while the vertical part (the Faddeev-Popov ghost) corresponds to the S field. The Vasiliev equations are then, respectively, the RG equations and the Becchi-Rouet-Stora-Tyutin equations, with the RG beta functions encoding bulk interactions. Finally, we remark that a large class of interacting field theories can be studied through integral transforms of our results, and it is natural to organize this in terms of a large N expansion.

Original language | English (US) |
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Article number | 106012 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 89 |

Issue number | 10 |

DOIs | |

State | Published - May 28 2014 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*89*(10), [106012]. https://doi.org/10.1103/PhysRevD.89.106012