An invitation to higher gauge theory

被引:132
作者
Baez, John C. [1 ]
Huerta, John [1 ]
机构
[1] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA
关键词
Category; Gerbe; Higher gauge theory; String; 2-category; 2-group; DEGREE-4 CHARACTERISTIC CLASSES; HIDDEN QUANTUM-GRAVITY; DIFFERENTIAL GEOMETRY; PARALLEL TRANSPORT; BUNDLE GERBES; LINE BUNDLES; INTEGRATION; CONNECTIONS; CATEGORIES; HOLONOMY;
D O I
10.1007/s10714-010-1070-9
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar, 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group', and the Lie 3-superalgebra that governs 11-dimensional supergravity.
引用
收藏
页码:2335 / 2392
页数:58
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