Rényi entropies for free éld theories

Igor R. Klebanov, Silviu S. Pufu, Subir Sachdev, Benjamin R. Safdi

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96 Scopus citations


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 languageEnglish (US)
Article number074
JournalJournal of High Energy Physics
Issue number4
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Field Theories in Higher Dimensions
  • Statistical Methods


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