Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane
arXiv:1906.07417 · doi:10.1007/s00220-021-03951-0
Abstract
The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows by a twisted/parametrized generalization of the Hopf invariant, after identifying the full 6d Hopf-Wess-Zumino term with a twisted homotopy Whitehead integral formula, which we establish.
22 pages; v2 fixes a missing theta7-summand in intermediate formulas and has two remarks added, for clarification; v3 fixes typos and makes the slicing over the homotopy fiber space of chi_8 more explicit
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- The character map in (twisted differential) non-abelian cohomology
- Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector
- Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
- Flux Quantization
- Flux Quantization on 11-dimensional Superspace
- Flux Quantization on M5-branes
- Rational Homotopy Theory
- Fundamental weight systems are quantum states
- Higher Gauge Theory
- Flux Quantization on Phase Space
- Quantum Observables of Quantized Fluxes
- Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
- Differential cohomology (encyclopedia article)
- Engineering of Anyons on M5-Probes via Flux Quantization
- The Hidden M-Group
- Gauge potentials on the M5 brane in twisted equivariant cohomotopy
- Flux Quantization on M-Strings
- Mysterious Triality and the Exceptional Symmetry of Loop Spaces