Determine bulk operator product expansions in critical loop models

Establish explicit operator product expansions for bulk primary fields in two-dimensional critical loop models that are consistent with known bulk three-point functions and crossing symmetry, so that disc N-point functions can be computed from bulk OPEs.

Background

The paper employs analytic bootstrap for boundary correlators but emphasizes that a full solution on the disc would require knowledge of bulk OPEs. While three-point functions are known analytically for the bulk CFT of critical loop models, the authors note that the bulk OPEs are not determined, limiting the ability to build higher-point disc correlators from 1-point functions.

Clarifying bulk OPEs would resolve a foundational structural gap and enable systematic derivations of disc N-point functions using standard boundary CFT methods.

References

From the disc 1-point function, we could deduce any bulk N-point function on the disc using bulk OPEs [Lewellen]. However, in critical loop models, we know bulk 3-point functions [jnrr25], but we do not know bulk OPEs.

— Diagonal boundary conditions in critical loop models  (2512.10400 - Downing et al., 11 Dec 2025) in Introduction, Bulk 2-point function: bulk channel decomposition