Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

Carey, Alan L.; Johnson, Stuart; Murray, Michael K.; Stevenson, Danny; Wang, Bai-Ling

doi:10.1007/s00220-005-1376-8

Cited by 81 publications

(148 citation statements)

References 39 publications

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“…Carey, Johnson, Murray, Stevenson and Wang [15] introduced multiplicative S 1 -bundle gerbes over G and showed they correspond to elements of H 4 .BG/. We see from the above that a multiplicative bundle gerbe over G may instead be viewed as a central extension of smooth 2-groups.…”

Section: Stringn/ As An Extension Of Smooth 2-groupsmentioning

confidence: 86%

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

Schommer-Pries

2011

Geom. Topol.

126

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We provide a model of the String group as a central extension of finite-dimensional 2-groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a geometric incarnation of the bicategory of smooth stacks and generalizes the more naive 2-category of Lie groupoids, smooth functors and smooth natural transformations. In particular this notion of smooth 2-group subsumes the notion of Lie 2-group introduced by Baez and Lauda [5]. More precisely we classify a large family of these central extensions in terms of the topological group cohomology introduced by Segal [56], and our String 2-group is a special case of such extensions. There is a nerve construction which can be applied to these 2-groups to obtain a simplicial manifold, allowing comparison with the model of Henriques [23]. The geometric realization is an A 1 -space, and in the case of our model, has the correct homotopy type of String.n/. Unlike all previous models [58; 60; 33; 23; 7] our construction takes place entirely within the framework of finitedimensional manifolds and Lie groupoids. Moreover within this context our model is characterized by a strong uniqueness result. It is a canonical central extension of Spin.n/. 57T10, 22A22, 53C08; 18D10

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Section: Stringn/ As An Extension Of Smooth 2-groupsmentioning

confidence: 86%

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

Schommer-Pries

2011

Geom. Topol.

126

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“…This central extension is only possible if the first fractional Pontryagin class of P vanishes:

\frac{1}{2} p_{1} false(P false) = 0

. This class is the characteristic class of the Chern–Simons 2‐gerbe of P , and a string structure can be regarded as a principal

Spin (n)

‐bundle P with a trivialization of the Chern–Simons gerbe . The latter is essentially the content of the last equation of : the 3‐form H is the trivialization of

\frac{1}{2} p_{1} false(P false)

, with the inclusion of the Pontryagin class of the tangent bundle.…”

Section: Higher Gauge Theoriesmentioning

confidence: 99%

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

Sämann

2019

Fortschritte der Physik

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I summarize and discuss some recent results on formulating actions of six‐dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review crucial aspects of this framework, such as L∞‐algebras and corresponding kinematical data given by higher connections. We then show that there is a mathematically consistent non‐Abelian extension of the self‐dual string equation which satisfies many physical expectations. Our construction favors a particular higher gauge group leading us to higher principal bundles known as string structures. Using these, we manage to formulate a six‐dimensional action which shares many properties with the famous (2,0)‐theory but also still differs from it in some key points.

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“…We recall from [33] the construction of the Chern-Simons 2-gerbe CS M , whose characteristic class is CC(CS M ) = 1 2 p 1 (M). It uses the basic gerbe G bas over Spin(n), together with its multiplicative structure (M, α) described in Section 2.1.…”

Section: String Structures As Trivializationsmentioning

confidence: 99%

String geometry vs. spin geometry on loop spaces

Waldorf

2015

Journal of Geometry and Physics

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We introduce various versions of spin structures on free loop spaces of smooth manifolds, based on a classical notion due to Killingback, and additionally coupled to two relations between loops: thin homotopies and loop fusion. The central result of this article is an equivalence between these enhanced versions of spin structures on the loop space and string structures on the manifold itself. The equivalence exists in two settings: in a purely topological one and a in geometrical one that includes spin connections and string connections. Our results provide a consistent, functorial, one-to-one dictionary between string geometry and spin geometry on loop spaces.Comment: 54 pages. In v2 two errorneous lemmata (2.3.3 and 3.1.3) have been removed, with corresponding changes in Prop. 2.3.4 and Def. 3.1.4 (now Prop. 2.3.3 and Def. 3.1.3, respectively); otherwise minor changes. v3 comes with few minor changes and is the published versio

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Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

Cited by 81 publications

References 39 publications

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

Central extensions of smooth 2–groups and a finite-dimensional string 2–group

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

String geometry vs. spin geometry on loop spaces

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