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2024年10月30日
Chinese Physics C> 2017, Vol. 41> Issue(6) : 063103 DOI: 10.1088/1674-1137/41/6/063103

Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

  • 1.

     Dipartimento di Fisica, Universita degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy

  • We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by Δ. For the case of two short intervals on a complex plane, we expand the Rényi mutual information by the cross ratio x to order x2Δ+2. For the case of one interval on a torus with low temperature, we expand the Rényi entropy by q=exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order qΔ+2. To make the result meaningful, we require that the scaling dimension Δ cannot be too small. For two intervals on a complex plane we need Δ >1, and for one interval on a torus we need Δ >2. We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side, and find matches of gravity and CFT results.
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Jia-ju Zhang. Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT[J]. Chinese Physics C, 2017, 41(6): 063103. doi: 10.1088/1674-1137/41/6/063103
Jia-ju Zhang. Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT[J]. Chinese Physics C, 2017, 41(6): 063103.  doi: 10.1088/1674-1137/41/6/063103 shu
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Received: 2017-02-17
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    Supported by ERC Starting Grant 637844-HBQFTNCER

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Note on non-vacuum conformal family contributions to Rényi entropy in two-dimensional CFT

    Corresponding author: Jia-ju Zhang,
  • 1. Dipartimento di Fisica, Universita degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
  • Received Date: 2017-02-17
  • Available Online: 2017-06-05
Fund Project:  Supported by ERC Starting Grant 637844-HBQFTNCER

Abstract: We calculate the contributions of a general non-vacuum conformal family to Rényi entropy in two-dimensional conformal field theory (CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by Δ. For the case of two short intervals on a complex plane, we expand the Rényi mutual information by the cross ratio x to order x2Δ+2. For the case of one interval on a torus with low temperature, we expand the Rényi entropy by q=exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order qΔ+2. To make the result meaningful, we require that the scaling dimension Δ cannot be too small. For two intervals on a complex plane we need Δ >1, and for one interval on a torus we need Δ >2. We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side, and find matches of gravity and CFT results.

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