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PreprintCC BY 4.0arXiv

Defect flows from functional relations in the asymptotic semiring

  • Federico Ambrosino
  • Anatoly Konechny
  • Ingo Runkel
  • Gérard M. T. Watts
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Abstract

We study perturbations of topological defects by a relevant holomorphic defect field in two-dimensional conformal field theory. This produces translation invariant defects and these necessarily flow to topological defects in the infrared. Translation invariant defects form a monoidal category which extends the fusion category of topological defects. We argue that the renormalisation group flow defines a semiring homomorphism from the semiring of translation invariant defects to an "asymptotic semiring" which we construct from topological defects. The semiring homomorphism preserves functional relations, and we illustrate in the example of Virasoro minimal models that the resulting relations in the asymptotic semiring constrain the defect flow endpoints. The companion paper [1] contains a detailed study of such defect flows in several minimal models, both numerically and analytically.

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Cite

BibTeXRIS
BibTeX
@misc{ambrosino2026defect,
  title = {{Defect flows from functional relations in the asymptotic semiring}},
  author = {Federico Ambrosino and Anatoly Konechny and Ingo Runkel and Gérard M. T. Watts},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30242},
  eprint = {2610.30242},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30242},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Defect flows from functional relations in the asymptotic semiring
AU  - Federico Ambrosino
AU  - Anatoly Konechny
AU  - Ingo Runkel
AU  - Gérard M. T. Watts
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30242
UR  - https://arxiv.org/abs/2610.30242
AB  - We study perturbations of topological defects by a relevant holomorphic defect field in two-dimensional conformal field theory. This produces translation invariant defects and these necessarily flow to topological defects in the infrared. Translation invariant defects form a monoidal category which extends the fusion category of topological defects. We argue that the renormalisation group flow defines a semiring homomorphism from the semiring of translation invariant defects to an "asymptotic semiring" which we construct from topological defects. The semiring homomorphism preserves functional relations, and we illustrate in the example of Virasoro minimal models that the resulting relations in the asymptotic semiring constrain the defect flow endpoints. The companion paper [1] contains a detailed study of such defect flows in several minimal models, both numerically and analytically.
ER  -