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

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Main Authors: Sati, Hisham, Schreiber, Urs
Format: Preprint
Published: 2019
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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
id 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