SciPost Physics

SciPost Phys. 13, 029 (2022) · published 19 August 2022

• doi: 10.21468/SciPostPhys.13.2.029
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

Many applications of fusion categories, particularly in physics, require the associators or $F$-symbols to be known explicitly. Finding these matrices typically involves solving vast systems of coupled polynomial equations in large numbers of variables. In this work, we present an algorithm that allows associator data for some category with unknown associator to be computed from a Morita equivalent category with known data. Given a module category over the latter, we utilize the representation theory of a module tube category, built from the known data, to compute this unknown associator data. When the input category is unitary, we discuss how to ensure the obtained data is also unitary. We provide several worked examples to illustrate this algorithm. In addition, we include several Mathematica files showing how the algorithm can be used to compute the data for the Haagerup category $\mathcal{H}_1$, whose data was previously unknown.

• Magdalena de la Fuente et al., Bulk-to-boundary anyon fusion from microscopic models
  64, 111904 (2023) [Crossref]
• Lu et al., On triality defects in 2d CFT
  J. High Energ. Phys. 2023, 173 (2023) [Crossref]
• Choi et al., Remarks on boundaries, anomalies, and noninvertible symmetries
  Phys. Rev. D 108, 125005 (2023) [Crossref]
• Bridgeman et al., Invertible Bimodule Categories and Generalized Schur Orthogonality
  Commun. Math. Phys. 402, 2691 (2023) [Crossref]