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arXiv · 2512.10400

Reflecting boundary conditions in critical loop models

Max Downing·Jesper Lykke Jacobsen·Rongvoram Nivesvivat·Sylvain Ribault·Hubert Saleur
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Abstract

In critical loop models, we call a boundary sticky if loops can attach to it, and reflecting otherwise. Using analytic bootstrap methods, we show that reflecting boundaries are characterised by one complex parameter, analogous to the boundary cosmological constant in Liouville theory. We determine disc 1-point functions, and write an explicit formula for disc 2-point functions as infinite combinations of conformal blocks. We also sketch the lattice interpretation of reflecting boundaries.

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Max Downing, Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur. 2026-09-21. Reflecting boundary conditions in critical loop models. https://arxiv.org/abs/2512.10400

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