TL;DR
This paper presents a unified elementary method to construct fusion rings for all affine Kac-Moody algebras, linking them to modular S-matrices and extending known results to twisted cases.
Contribution
It introduces a general elementary procedure for attaching fusion rings to any affine Kac-Moody algebra, including twisted cases, and relates these to the modular S-matrix.
Findings
Fusion rings are attached to all affine Kac-Moody algebras.
The method recovers known fusion rings for untwisted cases.
Twisted fusion rings are characterized via diagram automorphisms.
Abstract
In this note we describe a general elementary procedure to attach a fusion ring to any Kac-Moody algebra of affine type. In the case of untwisted affine algebras, they are usual fusion rings in the literature. In the case of twisted affine algebras, they are exactly the twisted fusion rings defined by the author in [Ho2] via tracing out diagram automorphisms on conformal blocks for appropriate simply-laced Lie algebras. We also relate the fusion ring to the modular S-matrix for any Kac-Moody algebra of affine type.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.