Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams

Abstract

We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by ordered configurations of points in the transversal 3-space. Then we show that the higher (co-)observables on these brane moduli, conceived as the (co-)homology of the Cohomotopy cocycle space, are given by weight systems on horizontal chord diagrams and reflect a multitude of effects expected in the microscopic quantum theory of Dp/D(p+2)-brane intersections: condensation to stacks of coincident branes and their Chan-Paton factors, BMN matrix model and fuzzy funnel states, M2-brane 3-algebras, the Hanany-Witten rules, AdS3-gravity observables, supersymmetric indices of Coulomb branches as well as gauge/gravity duality between all these. We discuss this in the context of the hypothesis that the M-theory C-field is charge-quantized in Cohomotopy theory.

62 pages; v2: section 4 expanded and introduction re-arranged; v3: discussion of M2/M5-brane states added

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• Twisted Cohomotopy implies twisted String structure on M5-branes
• Twisted Cohomotopy implies M5-brane anomaly cancellation
• M/F-Theory as Mf-Theory
• Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
• Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Flux Quantization
• Topological Quantum Gates in Homotopy Type Theory
• Flux Quantization on M5-branes
• Fundamental weight systems are quantum states
• Flux Quantization on Phase Space
• Cyclification of Orbifolds
• Quantum Observables of Quantized Fluxes
• Proper Orbifold Cohomology
• Differential cohomology (encyclopedia article)
• Differential Cohomology: Categories, Characteristic Classes, and Connections