Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
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| Format: | Preprint |
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2019
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| _version_ | 1866910319132016640 |
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| author | Sati, Hisham Schreiber, Urs |
| author_facet | Sati, Hisham Schreiber, Urs |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_10425 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams Sati, Hisham Schreiber, Urs High Energy Physics - Theory Algebraic Topology Geometric Topology Quantum Algebra 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. |
| title | Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams |
| topic | High Energy Physics - Theory Algebraic Topology Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/1912.10425 |