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The analytic bootstrap equations of non-diagonal two-dimensional CFT

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arxiv 1711.08916 v2 pith:LVPDXDJK submitted 2017-11-24 hep-th

Santiago Migliaccio , Sylvain Ribault This is my paper · ORCID
classification hep-th
keywords cftsfour-pointnon-diagonalbootstrapclassconformalequationsfields
verification ladder T0 review T1 audit T2 compute T3 formal
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Under the assumption that degenerate fields exist, diagonal CFTs such as Liouville theory can be solved analytically using the conformal bootstrap method. Here we generalize this approach to non-diagonal CFTs, i.e. CFTs whose primary fields have nonzero conformal spins. Assuming generic values of the central charge, we find that the non-diagonal sector of the spectrum must be parametrized by two integer numbers. We then derive and solve the equations that determine how three- and four-point structure constants depend on these numbers. In order to test these results, we numerically check crossing symmetry of a class of four-point functions in a non-rational limit of D-series minimal models. The simplest four-point functions in this class were previously argued to describe connectivities of clusters in the critical Potts model.

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Cited by 3 Pith papers

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

  1. Toward the Structure Constants of $\mathcal{N}=2$ Liouville Theory

    hep-th 2026-07 conditional novelty 7.0 of 10

    N=2 Liouville structure constants are proposed via mirror symmetry to the SL(2)_k/U(1) supercoset, with angular-momentum-violating sectors given explicitly and tested semiclassically to leading loop order.

  2. Logarithmic operators in $c=0$ bulk CFTs

    hep-th 2024-11 conditional novelty 7.0 of 10

    The bulk energy four-point function in percolation and self-avoiding walk CFTs is non-zero at c=0, driven by coupling to a rank-3 Jordan block associated with the second energy operator.

  3. Exactly solvable conformal field theories

    hep-th 2024-11 conditional novelty 3.0 of 10

    A lecture-note review unifying the exactly solvable 2d CFTs without extended chiral symmetry under the bootstrap framework, with a conjectural roadmap for solving the loop CFTs.

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