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New Properties of Large-$c$ Conformal Blocks from Recursion Relation

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arxiv 1804.06171 v4 pith:MBGSL7BE submitted 2018-04-17 hep-th cond-mat.stat-mech

Yuya Kusuki This is my paper · ORCID
classification hep-thcond-mat.stat-mech
keywords blockslargeconformalfinddimensionsstatesheavyintermediate
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We study large $c$ conformal blocks outside the known limits. This work seems to be hard, but it is possible numerically by using the Zamolodchikov recursion relation. As a result, we find new some properties of large $c$ conformal blocks with a pair of two different dimensions for any channel and with various internal dimensions. With light intermediate states, we find a Cardy-like asymptotic formula for large $c$ conformal blocks and also we find that the qualitative behavior of various large $c$ blocks drastically changes when the dimensions of external primary states reach the value $c/32$. And we proceed to the study of blocks with heavy intermediate states $h_p$ and we find some simple dependence on heavy $h_p$ for large $c$ blocks. The results in this paper can be applied to, for example, the calculation of OTOC or Entanglement Entropy. In the end, we comment on the application to the conformal bootstrap in large $c$ CFTs.

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Cited by 3 Pith papers

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  1. Phase transition from eigenstate thermalization: forbidden singularity and instanton proliferation via AGT correspondence

    hep-th 2026-08 conditional novelty 6.0 of 10

    Forbidden singularities in heavy-light Virasoro blocks are shown to be the critical point of an instanton-gas phase transition via AGT, with critical fugacity equal to the known singularity location.

  2. Entanglement Entropy after Double-Excitation as Interaction Measure

    hep-th 2019-08 conditional novelty 6.0 of 10

    For double local operator excitations in pure 2D CFTs, the late-time entanglement entropy equals the sum of two single-quench results plus a negative c/6 log((l_B - l_A)/(t - l_A)) interaction term.

  3. Modern Approach to 2D Conformal Field Theory

    hep-th 2024-12 unverdicted novelty 1.0 of 10

    A review-style lecture note collection presenting modern bootstrap methods for irrational 2D CFTs, with no new research results.

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