John Baez

Joint mathematics/physics talk at Louisiana State University, November 16, 2006
Mathematics colloquium at Stanford University, December 7, 2006.

Higher Gauge Theory

Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1-dimensional extended objects: paths or loops in space. This suggests that we seek some sort of "higher gauge theory" that describes parallel transport as we move a path through space, tracing out a surface. To find the right mathematical language for this, we must "categorify" concepts from topology and geometry, replacing Lie groups by Lie 2-groups, bundles by 2-bundles, and so on. Some interesting examples of these concepts show up in the mathematics of topological quantum field theory, string theory and 11-dimensional supergravity.

• Higher Gauge Theory - in PDF and Postscript

• John Baez and Aaron Lauda, Higher-Dimensional Algebra V: 2-Groups
• John Baez and Alissa Crans, Higher-Dimensional Algebra VI: Lie 2-Algebras
• John Baez and Urs Schreiber, Higher Gauge Theory
• John Baez, Alissa Crans, Urs Schreiber and Danny Stevenson, From Loop Groups to 2-Groups
• Toby Bartels, Higher Gauge Theory I: 2-Bundles
• Urs Schreiber, From Loop Space Mechanics to Nonabelian Strings

• Urs Schreiber, Chern-Simons Lie 3-Algebra Inside Derivations of String Lie 2-Algebra

• Paolo Aschieri and Branislaw Jurco, Gerbes, M5-brane Anomalies and E₈ Gauge Theory
• Leonardo Castellani, Lie Derivatives along Antisymmetric Tensors, and the M-Theory Superalgebra
• Pietro Fré and Pietro Antonio Grassi, Pure Spinors, Free Differential Algebras, and the Supermembrane
• Urs Schreiber, SuGra 3-Connection Reloaded

For other work on higher gauge theory, see:

• Roger Picken and Marco Mackaay, Holonomy and Parallel Transport for Abelian Gerbes
• Lawrence Breen and William Messing, Differential Geometry of Gerbes
• Marco Mackaay, A Note on the Holonomy of Connections in Twisted Bundles
• Hendryk Pfeiffer, Higher Gauge Theory and a Non-Abelian Generalization of 2-Form Electrodynamics
• Florian Girelli and Hendryk Pfeiffer, Higher Gauge Theory - Differential Versus Integral Formulation
• André Henriques, Integrating L_∞-Algebras

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