John Baez

Workshop on Poisson Geometry and Sigma Models, Erwin Schrödinger Institute

August 22, 2007

Higher Gauge Theory and the String Group

Higher gauge theory is a generalization of gauge theory that describes the parallel transport not just of particles, but also strings or higher-dimensional branes. To handle strings, we categorify familiar notions from gauge theory and consider "principal 2-bundles" with a given "structure 2-group". These are a slight generalization of nonabelian gerbes. We focus on examples related to the 2-group String_k(G) associated to any compact simple Lie group G. We describe how this 2-group is built using the level-k central extension of the loop group of G, and how it is related to the "string group". Finally, we discuss 2-bundles with String_k(G) as structure 2-group, and pose the problem of computing characteristic classes for such 2-bundles in terms of connections.

Click on this to see the transparencies of the talk:

• Higher Gauge Theory and the String Group - 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, How to Get a Spinning String from Here to There
• Urs Schreiber, On 2-Representations and 2-Vector Bundles

• Stefan Stolz and Peter Teichner, What Is an Elliptic Object?, Section 5: String Structures and Connections

• Paolo Aschieri, Luigi Cantini, and Branislav Jurco, Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory
• Paolo Aschieri and Branislaw Jurco, Gerbes, M5-brane Anomalies and E₈ Gauge Theory
• Lawrence Breen and William Messing, Differential Geometry of Gerbes
• Branislaw Jurco, Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry
• André Henriques, Integrating L_∞-Algebras

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