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Bootstrapping boundary-localized interactions

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arxiv 2009.03336 v2 pith:YE2F23PT submitted 2020-09-07 hep-th cond-mat.str-el

Connor Behan , Lorenzo Di Pietro , Edoardo Lauria , Balt C. van Rees This is my paper · ORCID
classification hep-thcond-mat.str-el
keywords boundaryconformalbulkconditionconditionsfieldfindpair
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We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a `shadow pair' of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a `kink' in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

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  1. The Bootstrap of Points and Lines

    hep-th 2025-06 accept novelty 8.0 of 10

    A mixed-correlator bootstrap for 2D boundary CFTs produces new rigorous bounds on boundary entropy, bulk-to-boundary OPE coefficients, and gap spectra, tested on Ising and free boson and applied to su(2)_2 WZW.

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