2018/10/01 by Rafał R. Suszek, Suszek, Rafał R.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1810.00856
openalex publication_date 2018/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is another step towards a realisation of the goal, advanced in articles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematic supersymmetry-equivariant geometrisation of physically distinguished Green-Schwarz super-(p+2)-cocycles defining classes in the supersymmetry-invariant refinement of the de Rham cohomology of homogeneous spaces of (supersymmetry) Lie supergroups, associated with reductive decompositions of their Lie superalgebras. It deals with a correlated geometrisation of a pair of such super-(p+2)-cocycles on spaces in correspondence under a blow-up transformation dual to the İnönü-Wigner contraction that relates the respective (supersymmetry) Lie superalgebras, the latter correspondence being taken as the organising principle of the geometrisation procedure that exploits the link between the Cartan-Eilenberg cohomology of the supersymmetry group and the Chevalley-Eilenberg cohomology of its Lie superalgebra, alongside a cohomological classification of central extensions thereof. A general scheme of a correlated geometrisation compatible with the contraction is laid out and illustrated on the nontrivial example of a pair of consistent super-0-brane backgrounds: the super-Minkowski space sMink3,1|8 with the standard N=2 Green-Schwarz super-2-cocycle on it and the super-AdS2 × S2 space with Zhou's super-2-cocycle on it, asymptoting to the former in the limit of an infinite common radius of the AdS2 and the S2 in the body AdS2× S2 of the supertarget. The geometrisation yields the respective supersymmetry-equivariant super-0-gerbes, i.e., the prequantum bundles of the associated Green-Schwarz super-σ-models in the Nambu-Goto formulation. Upon passing to the equivalent Hughes-Polchinski formulation of the models, the relevant extended super-0-gerbes are verified to possess a weak κ-equivariant structure.