Semistrict Higher Gauge Theory

Abstract

We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Cech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Severa. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian N=(2,0) tensor multiplet taking values in a semistrict Lie 2-algebra.

v4: 76 pages, minor errors fixed, published version

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Cited by in corpus (23)

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• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• Towards an M5-Brane Model II: Metric String Structures
• Adjusted Parallel Transport for Higher Gauge Theories
• Non-abelian Gerbes and Enhanced Leibniz Algebras
• $L_{\infty }$-Algebra Models and Higher Chern-Simons Theories
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• A Lie based 4-dimensional higher Chern-Simons theory
• Generalized Yang-Mills Theory and Gravity
• Generalized Higher Gauge Theory
• Higher Poincare Lemma and Integrability
• Topological invariant of 4-manifolds based on a 3-group
• Algebraic formulation of higher gauge theory
• Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory
• Higher geometry for non-geometric T-duals
• Higher Gauge Theory
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• Explicit Non-Abelian Gerbes with Connections
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity