Higher gauge theory

By John C. Baez, Urs Schreiber. 2005

232 citations recorded by the source corpus.

Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings) using 2-connections on 2-bundles. A 2-bundle is a categorified version of a bundle: that is, one where the fiber is not a manifold but a category with a suitable smooth structure. Where gauge theory uses Lie groups and Lie algebras, higher gauge theory uses their categorified analogues: Lie 2-groups and Lie 2-algebras. We describe a theory of 2-connections on principal 2-bundles and explain how this is related to Breen and Messing's theory of connections on nonabelian gerbes. The distinctive feature of our theory is that a 2-connection allows parallel transport along paths and surfaces in a parametrization-independent way. In terms of Breen and Messing's framework, this requires that the "fake curvature" must vanish. In this paper we summarize the main results of our theory without proofs.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9397007202e7fca55f3384032fe91b08b3937bce

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Citations in the corpus

Twisted Differential String and Fivebrane Structures (2009, background): “In low categorical dimension this reproduces the description in [10, 72, 74].”
Selfdual strings and loop space Nahm equations (2008, methodology): “In [11], [12] a gerbe formalism was developed with ultra local expressions for non-abelian loop space gauge fields as defined in [13] based on ideas in [14].”
“What is a Thing?”: Topos Theory in the Foundations of Physics (2008, background): “For example, Baez’s advocation of n-categories [5, 6]; ‘categorial quantum theory’ [2, 73]; Takeuti’s theory(19) of ‘quantum sets’ [71]; and Crane’s work on categorial models of space-time [17].”
From loop groups to 2-groups (2005, background): “There is a theory of ‘2-bundles’ in which a Lie 2-group plays the role of structure group [ 4 , 5]. Connections on 2-bundles describe parallel transport of 1-dimensional extended objects; e.g.”
The Classifying Space of a Topological 2-Group (2008, background): “ecent work in higher gauge theory has revealed the importance of categorifying the theory ofbundles and considering‘2-bundles’, where the ﬁber is a topological category instead of a topological space [5]. These structures show up not only in mathematics, where they form a useful generalization of no”
Convenient Categories of Smooth Spaces (2008, background): “This work had its origin in collaborations between the first author, Urs Schreiber [3, 4] and Toby Bartels [5].”
On 2-group global symmetries and their anomalies (2018, methodology): “For theories with 2-group global symmetry the appropriate background fields are connections forming a 2-group gauge theory [6, 8].”
Reparametrizations of continuous paths (2007, background): “Further possible areas of application of the results (and of higher-dimensionsal generalisations still to be investigated) include categorical homotopy theory as in [8], categorified gauge theory as in [1] and n-transport theory; cf.”
An invitation to higher gauge theory (2010, methodology): “For these, the reader can turn to Section 2.1 of Schreiber and Waldorf [87].”
Parallel Transport and Functors (2007, background): “l transport. Transport functors have a natural generalization to transport nfunctors. In particular the case n = 2 promises relations between transport 2-functors and gerbes with connective structure [BS07], similar to the relation between transport 1-functors and bundles with connections presented ”