### Abstract

Rényi entropies Sq are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q ≥ 0. For (d + 1)-dimensional conformal éld theories, the Rényi entropies across Sd-1 may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R×H ^{d}, is where Hd the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+1)-dimensional sphere and S1×Hd, respectively. We calculate the Rényi entropies of free massless scalars and fermions in d = 2, and show how using zeta-function regularization onefinds agreement between the calculations on the branched coverings of S ^{3} and on S ^{1} × H ^{2}. Analogous calculations for massive free élds provide monotonic nterpolating functions between the Rényi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Rényi entropy calculations in d < 2.

Original language | English (US) |
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Article number | 074 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 4 |

DOIs | |

State | Published - May 2 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- Field Theories in Higher Dimensions
- Statistical Methods

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## Cite this

*Journal of High Energy Physics*,

*2012*(4), [074]. https://doi.org/10.1007/JHEP04(2012)074