2018/08/13 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.1808.04470
openalex publication_date 2018/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a continuation of a programme, initiated in the work arXiv:1706.05682 [hep-th], of supersymmetry-equivariant geometrisation of the Green-Schwarz super-(p+2)-cocycles coupling to the topological charges carried by super-p-branes of the superstring theory on reductive homogeneous spaces of supersymmetry Lie supergroups. In the present part, the ideas and geometro-algebraic tools developed previously are substantially enhanced, adapted to and applied in the physically significant curved backround of Metsaev and Tseytlin, determining the propagation of the critical superstring in the super-\rm AdS5×\mathbbS5 geometry. The analysis brings to the fore the rôle, in the geometrisation scheme proposed, of the wrapping anomaly of the Poisson algebra of the Noether charges of the rigid symmetries of the relevant super-σ-model that lift the geometric symmetries of the supertarget. In particular, the significance of the charges quantifying the monodromy of the Grassmann-odd coordinates in the Kostelecký-Rabin-type quotient of the supertarget is emphasised. A trivial super-1-gerbe is associated with the Metsaev-Tseytlin super-3-cocycle over the super-\rm AdS5×\mathbbS5 target. The issue of compatibility of the geometrisation with the İnönü-Wigner contraction of the supersymmetry Lie superalgebra to its flat-superspace counterpart is investigated at some length, revealing the rigidity of the relevant Cartan-Eilenberg cohomology and signalling an attractive potential alternative to the non-contractible trivial super-1-gerbe constructed.