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Constraining boundary conditions in nonrational CFTs

Yucong Cai, Daniel Robbins, and Hassaan Saleem

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Phys. Rev. D 113, 106017 – Published 18 May, 2026

DOI: https://doi.org/10.1103/44rr-dz2y

Abstract

We revisit the question of conformal boundary conditions in the compact free boson CFT in two dimensions. Besides the well-known Neumann and Dirichlet cases, there is an additional proposed one-parameter family of boundary states when the radius is an irrational multiple of the self-dual radius. These additional states have a continuous open string spectrum, and we give an explicit formula for the density of states. We also discuss several pathologies of these states, including the possible violation of the cluster condition, and that they have a divergent g function.

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Phys. Rev. D 113, 106017– Published 18 May, 2026
  • Received 9 April 2025
  • Accepted 30 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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