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A universal feature of CFT Renyi entropy

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arxiv 1308.1083 v3 pith:TFP2YYVO submitted 2013-08-05 hep-th cond-mat.stat-mech

Eric Perlmutter This is my paper · ORCID
classification hep-thcond-mat.stat-mech
keywords entropyrenyicftscoefficientknowledgeacrossadditionapplicable
verification ladder T0 review T1 audit T2 compute T3 formal
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We show that for a d-dimensional CFT in flat space, the Renyi entropy S_q across a spherical entangling surface has the following property: in an expansion around q=1, the first correction to the entanglement entropy is proportional to C_T, the coefficient of the stress tensor vacuum two-point function, with a fixed d-dependent coefficient. This is equivalent to a similar statement about the free energy of CFTs living on S^1 x H^{d-1} with inverse temperature \beta=2\pi q. In addition to furnishing a direct argument applicable to all CFTs, we exhibit this result using a handful of gravity and field theory computations. Knowledge of C_T thus doubles as knowledge of Renyi entropies in the neighborhood of q=1, which we use to establish new results in 3d vector models at large N.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cosmological higher-curvature gravities

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    Higher-curvature gravities are constructed in which both FLRW backgrounds and linearized scalar perturbations obey at most second-order differential equations.

  2. Universal relation between $C_{T}$ and the CFT Weyl anomaly

    hep-th 2026-02 conditional novelty 6.0 of 10

    In any even-dimensional CFT, C_T = [d/(d−1)]·[(d+1)!/(d/2−1)!]·c, where c is the coefficient of the quadratic-in-Weyl term in the trace anomaly.

  3. Diamonds in the Bulk and Large-$N$ Scaling in AdS/CFT

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    Bulk field algebras of causal diamonds in AdS/CFT require a double-scaling limit, so sub-AdS-radius distances are not described by bulk QFT.

  4. A thermofield-double model of Uhlmann anholonomy

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    For a thermofield double model, Uhlmann parallel transport acts as optimal filtering measurements on one side and as holonomic quantum gates on the other, with an iSWAP gate constructible from geodesic triangles.

  5. Effective density matrix for vacua in asymptotically flat gravity

    hep-th 2025-09 conditional novelty 5.0 of 10

    The vacuum of a large causal diamond in asymptotically flat gravity is claimed to be a Gaussian in the supertranslation Goldstone mode, giving modular Hamiltonian variance A/epsilon squared.

  6. Hilbert Bundles and Holographic Space-time: the Hydrodynamic Approach to Gravity

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    Einstein's equations are treated as hydrodynamic equations for the area-law entropy of causal diamonds, with quantum dynamics proposed to live in a Hilbert bundle over spacetime geodesics.

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