Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory

Abstract

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent formalism and in local coordinates. These are the gauge fields needed for the construction of Yang-Mills theories with 2-form gauge potential.

31 pages, final version, added one reference. To apper in CMP

References in corpus (4)

• Twisted K-theory and K-theory of bundle gerbes
• WZW branes and gerbes
• The universal gerbe, Dixmier-Douady class, and gauge theory
• TQFT's and gerbes

Cited by in corpus (42)

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• General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids
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• BRST, anti-BRST and gerbes
• BRST, anti-BRST and their geometry
• The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module
• Principal 2-bundles and their gauge 2-groups
• Semistrict Higher Gauge Theory
• On Twistors and Conformal Field Theories from Six Dimensions
• M-brane Models from Non-Abelian Gerbes
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• On $3$-gauge transformations, $3$-curvature and $\mathbf{Gray}$-categories
• Towards an M5-Brane Model II: Metric String Structures
• Adjusted Parallel Transport for Higher Gauge Theories
• Non-abelian Gerbes and Enhanced Leibniz Algebras
• Non-abelian higher gauge theory and categorical bundle
• Free Abelian 2-Form Gauge Theory: BRST Approach
• Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry
• A new kind of geometric phases in open quantum systems and higher gauge theory
• Infinitesimal 2-braidings and differential crossed modules
• From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets
• Higher Poincare Lemma and Integrability
• Higher geometry for non-geometric T-duals
• Towards an M5-Brane Model III: Self-Duality from Additional Trivial Fields
• Higher form Yang-Mills as higher BFYM theories
• Higher Gauge Theory
• 3-form Yang-Mills based on 2-crossed modules
• Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity
• On the global $2$-holonomy for a $2$-connection on a $2$-bundle
• Twisted-Product Categorical Bundles
• Higher Chern-Simons based on (2-)crossed modules
• Topological Quantum Field Theory on Non-Abelian Gerbes
• Atiyah sequence and Gauge transformations of a principal $2$-bundle over a Lie groupoid
• Chern correspondence for higher principal bundles
• On two notions of a Gerbe over a stack
• Explicit Non-Abelian Gerbes with Connections
• The first Pontryagin class of a quadratic Lie 2-algebroid
• A toy model for $p$-form gauge symmetry