Engineering of Anyons on M5-Probes via Flux Quantization
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arXiv
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| Format: | Preprint |
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2025
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| author | Sati, Hisham Schreiber, Urs |
| author_facet | Sati, Hisham Schreiber, Urs |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Engineering of Anyons on M5-Probes via Flux Quantization Sati, Hisham Schreiber, Urs High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V27, 81T30, 81V70, 20F36, Secondary: 55Nxx, 55Pxx, 55Qxx, 81T40, 57K16, 81P68, 81T45 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. |
| title | Engineering of Anyons on M5-Probes via Flux Quantization |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V27, 81T30, 81V70, 20F36, Secondary: 55Nxx, 55Pxx, 55Qxx, 81T40, 57K16, 81P68, 81T45 |
| url | https://arxiv.org/abs/2501.17927 |