Bulk-Edge Correspondence via Higher Gauge Theory
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arXiv
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| Format: | Preprint |
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2026
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| author | Sati, Hisham Schreiber, Urs |
| author_facet | Sati, Hisham Schreiber, Urs |
| contents | More profound than bulk topological order of quantum materials is only its unwinding via gapless excitations along boundaries of the sample. We recast this bulk-edge correspondence -- for the experimentally relevant case of fractional quantum Hall (FQH) systems -- in terms of effective relative higher gauge theory, controlled by choices of classifying fibrations. For FQH systems, we identify the complex Hopf fibration as classifying the bulk/boundary topological effects, and find that it yields a non-Lagrangian reconstruction of Floreanini-Jackiw/Wess-Zumino-Witten chiral edge currents.
Remarkably, the resulting effective FQH higher gauge theory turns out to be "geometrically engineered" on M2/M5-branes probing A-type orbi-singularities in 11D supergravity, globally completed by flux-quantization in twisted equivariant differential (TED) Cohomotopy: Here the M-string ends of M2-branes on M5-branes engineer the FQH liquid's boundary. This geometric engineering on M-branes might naturally elucidate the curious combination of $W_\infty$-symmetry and of super-symmetry that is known to govern the collective excitations of FQH liquids at long wavelengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10232 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bulk-Edge Correspondence via Higher Gauge Theory Sati, Hisham Schreiber, Urs High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V70, 55Q55, 81T70, Secondary: 83E50, 81T30, 18N60 More profound than bulk topological order of quantum materials is only its unwinding via gapless excitations along boundaries of the sample. We recast this bulk-edge correspondence -- for the experimentally relevant case of fractional quantum Hall (FQH) systems -- in terms of effective relative higher gauge theory, controlled by choices of classifying fibrations. For FQH systems, we identify the complex Hopf fibration as classifying the bulk/boundary topological effects, and find that it yields a non-Lagrangian reconstruction of Floreanini-Jackiw/Wess-Zumino-Witten chiral edge currents. Remarkably, the resulting effective FQH higher gauge theory turns out to be "geometrically engineered" on M2/M5-branes probing A-type orbi-singularities in 11D supergravity, globally completed by flux-quantization in twisted equivariant differential (TED) Cohomotopy: Here the M-string ends of M2-branes on M5-branes engineer the FQH liquid's boundary. This geometric engineering on M-branes might naturally elucidate the curious combination of $W_\infty$-symmetry and of super-symmetry that is known to govern the collective excitations of FQH liquids at long wavelengths. |
| title | Bulk-Edge Correspondence via Higher Gauge Theory |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Algebraic Topology Quantum Physics Primary: 81V70, 55Q55, 81T70, Secondary: 83E50, 81T30, 18N60 |
| url | https://arxiv.org/abs/2605.10232 |