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Holographic R磂nyi entropy for two-dimensional N=(2,2) superconformal field theory

Zhibin Li; Jia-ju ZhangSubjects: Physics >> General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

We investigate the holographic R?enyi entropy for two-dimensional N = (2, 2) superconformal field theory (SCFT), which is dual to N = 2 supergravity in AdS3 background. In SCFT we have the stress tensor,current, and their supersymmetric partners, and in supergravity we have the graviton, vector field, and two gravitinos. We get the R?enyi mutual information of two short intervals on complex plane in expansion by the cross ratio x to order x4, and R?enyi entropy of one interval on torus in expansion by q = exp(?2 /L), with being the inverse temperature and L being the spatial period, to order q2. We calculate in both the supergravity and SCFT sides, and find matches of the results. |

Short interval expansion of R\'enyi entropy on torus

Bin Chen; Jun-Bao Wu; Jia-ju ZhangSubjects: Physics >> Nuclear Physics

We investigate the short interval expansion of the R\'enyi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval???to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the R\'enyi entropy at any temperature. In particular, we pay special attention to the large?c?CFTs dual to the AdS3?gravity and its cousins. At both low and high temperature limits, we read the R\'enyi entropies to order??6, and find good agreements with holographic results. Moreover, the expansion allows us to read?1/c?contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well. |

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