The work constructs adjusted connections on non-abelian bundle gerbes classified by Saemann's adjusted non-abelian differential cohomology and provides a new coordinate-free version of Tellez-Dominguez' lifting theorem to abelian 2-gerbes.
A global perspective to connections on principal 2-bundles
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen-Messing. This provides a consistent, global perspective to higher gauge theory.
verdicts
UNVERDICTED 3representative citing papers
Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.
citing papers explorer
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Adjusted connections on non-abelian bundle gerbes
The work constructs adjusted connections on non-abelian bundle gerbes classified by Saemann's adjusted non-abelian differential cohomology and provides a new coordinate-free version of Tellez-Dominguez' lifting theorem to abelian 2-gerbes.
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Operational total space theory of principal 2-bundles II: 2-connections and 1- and 2--gauge transformations
Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
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On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials
Constructs Čech-de Rham bicomplex from gerbe data for BV-BRST complex and anomaly descent of U(1) 1-form symmetries in Maxwell theory.