Infinite-dimensional algebraic \(\mathfrak{Spin}(N)\) structure in extended/higher dimensional SUSY holoraumy for valise and on shell supermultiplet representations. (English) Zbl 1522.81634
Summary: We explore the relationship between holoraumy and Hodge duality beyond four dimensions. We find this relationship to be ephemeral beyond six dimensions: it is not demanded by the structure of such supersymmetrical theories. In four dimensions for the case of the vector-tensor \(\mathcal{N} = 4\) multiplet, however, we show that such a linkage is present. Reduction to 1D theories presents evidence for a linkage from higher-dimensional supersymmetry to an infinite-dimensional algebra extending \(\mathfrak{Spin}(N)\).
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81T11 | Higher spin theories |
| 81Q60 | Supersymmetry and quantum mechanics |
| 83E50 | Supergravity |
| 81Q70 | Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory |
| 83E05 | Geometrodynamics and the holographic principle |
Software:
Adinkra.mReferences:
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