کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1851594 | 1528807 | 2015 | 6 صفحه PDF | دانلود رایگان |
In the presence of a sharp corner in the boundary of the entanglement region, the entanglement entropy (EE) and Rényi entropies for 3d CFTs have a logarithmic term whose coefficient, the corner function, is scheme-independent. In the limit where the corner becomes smooth, the corner function vanishes quadratically with coefficient σ for the EE and σnσn for the Rényi entropies. For a free real scalar and a free Dirac fermion, we evaluate analytically the integral expressions of Casini, Huerta, and Leitao to derive exact results for σ and σnσn for all n=2,3,…n=2,3,… . The results for σ agree with a recent universality conjecture of Bueno, Myers, and Witczak-Krempa that σ/CT=π2/24σ/CT=π2/24 in all 3d CFTs, where CTCT is the central charge. For the Rényi entropies, the ratios σn/CTσn/CT do not indicate similar universality. However, in the limit n→∞n→∞, the asymptotic values satisfy a simple relationship and equal 1/(4π2)1/(4π2) times the asymptotic values of the free energy of free scalars/fermions on the n-covered 3-sphere.
Journal: Physics Letters B - Volume 749, 7 October 2015, Pages 383–388