## Abstract

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2 + 1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2 + 1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.

Original language | English (US) |
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Article number | 1 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 7 |

DOIs | |

State | Published - 2012 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- AdS-CFT correspondence
- Field theories in lower dimensions
- Renormalization group