Engineering of Anyons on M5-Probes via Flux Quantization

• URL: http://arxiv.org/abs/2501.17927v1
• Date: Wed, 29 Jan 2025 19:00:04 GMT
• Title: Engineering of Anyons on M5-Probes via Flux Quantization
• Authors: Hisham Sati, Urs Schreiber,
• Abstract summary: We develop a novel derivation of anyonic topological order on single magnetized M5-branes. The rigorous construction is non-Lagrangian and non-perturbative. Results imply from this the quantum observables and modular functor of abelian Chern-Simons theory.
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• Abstract: These extended lecture notes survey a novel derivation of anyonic topological order (as seen in fractional quantum Hall systems) on single magnetized M5-branes probing Seifert orbi-singularities ("geometric engineering" of anyons), which we motivate from fundamental open problems in the field of quantum computing. The rigorous construction is non-Lagrangian and non-perturbative, based on previously neglected global completion of the M5-brane's tensor field by flux-quantization consistent with its non-linear self-duality and its twisting by the bulk C-field. This exists only in little-studied non-abelian generalized cohomology theories, notably in a twisted equivariant (and "twistorial") form of unstable Cohomotopy ("Hypothesis H"). As a result, topological quantum observables form Pontrjagin homology algebras of mapping spaces from the orbi-fixed worldvolume into a classifying 2-sphere. Remarkably, results from algebraic topology imply from this the quantum observables and modular functor of abelian Chern-Simons theory, as well as braid group actions on defect anyons of the kind envisioned as hardware for topologically protected quantum gates.

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