Irreducible differential spinors on Lorentzian four-manifolds are reformulated via parabolic pairs and isotropic parallelisms, yielding characterizations of torsion parallel spinors, supersymmetric NS-NS solutions, and an evolution flow compatibility theorem.
$\infty$-Bundles
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abstract
Higher bundles are homotopy coherent generalisations of classical fibre bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group gauge theories with higher-form gauge potentials and their higher-dimensional holonomies. An $\infty$-categorical formulation of higher bundles further allows one to identify these objects in contexts outside the worlds of smooth manifolds or topological spaces. This article reviews the theory of $\infty$-bundles, focussing on principal $\infty$-bundles, and surveys several of their applications. It is an invited contribution to the Topology section in the second edition of the Encyclopedia of Mathematical Physics.
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2025 1verdicts
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Torsion parallel spinors on Lorentzian four-manifolds and supersymmetric evolution flows on bundle gerbes
Irreducible differential spinors on Lorentzian four-manifolds are reformulated via parabolic pairs and isotropic parallelisms, yielding characterizations of torsion parallel spinors, supersymmetric NS-NS solutions, and an evolution flow compatibility theorem.