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Differential cohomology in a cohesive ∞topos
"... We formulate differential cohomology and ChernWeil theory the theory of connections on fiber bundles and of gauge fields abstractly in the context of a certain class of higher toposes that we call cohesive. Cocycles in this differential cohomology classify higher principal bundles equipped with c ..."
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We formulate differential cohomology and ChernWeil theory the theory of connections on fiber bundles and of gauge fields abstractly in the context of a certain class of higher toposes that we call cohesive. Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive structure (topological, smooth, synthetic differential, supergeometric, etc.) and equipped with connections. We discuss various models of the axioms and wealth of applications revolving around fundamental notions and constructions in prequantum field theory and string theory. In particular we show that the cohesive and differential refinement of universal characteristic cocycles constitutes a higher ChernWeil homomorphism refined from secondary caracteristic classes to morphisms of higher moduli stacks of higher gauge fields, and at the same time constitutes extended geometric prequantization – in the sense of extended/multitiered quantum field theory – of higher dimensional ChernSimonstype field theories and WessZuminoWittentype field theories. This document, and accompanying material, is kept online at ncatlab.org/schreiber/show/differential+cohomology+in+a+cohesive+topos 1 We formulate differential cohomology and ChernWeil theory the theory of connections on fiber bundles
AKSZ models of semistrict higher gauge theory
 JHEP 1303, 014 (2013) [arXiv:1112.2819 [hepth
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A Construction of String 2Group Models using a TransgressionRegression Technique
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Integrating central extensions of Lie algebras via Lie 2groups
, 2014
"... The purpose of this paper is to show how central extensions of (possibly infinitedimensional) Lie algebras integrate to central extensions of étale Lie 2groups. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanis ..."
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Cited by 2 (2 self)
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The purpose of this paper is to show how central extensions of (possibly infinitedimensional) Lie algebras integrate to central extensions of étale Lie 2groups. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of pi2 for each finitedimensional Lie group. This fact was used by Cartan (in a slightly other guise) to construct the simply connected Lie group associated to each finitedimensional Lie algebra. In infinite dimensions, there is an obstruction for a central extension of Lie algebras to integrate to a central extension of Lie groups. This obstruction comes from nontrivial pi2 for general Lie groups. We show that this obstruction may be overcome by integrating central extensions of Lie algebras not to Lie groups but to central extensions of étale Lie 2groups. As an application, we obtain a generalization of Lie’s Third Theorem to infinitedimensional Lie algebras.
NonAbelian Tensor Multiplet Equations from Twistor Space
, 2012
"... We establish a Penrose–Ward transform yielding a bijection between holomorphic principal 2bundles over a twistor space and nonAbelian selfdual tensor fields on sixdimensional flat spacetime. Extending the twistor space to supertwistor space, we derive sets of manifestly N = (1, 0) and N = (2, ..."
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We establish a Penrose–Ward transform yielding a bijection between holomorphic principal 2bundles over a twistor space and nonAbelian selfdual tensor fields on sixdimensional flat spacetime. Extending the twistor space to supertwistor space, we derive sets of manifestly N = (1, 0) and N = (2, 0) supersymmetric nonAbelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for nonAbelian supersymmetric selfdual strings.