# Gerbes in Geometry, Field Theory, and Quantisation

@article{Bunk2021GerbesIG,
title={Gerbes in Geometry, Field Theory, and Quantisation},
author={Severin Bunk},
journal={Complex Manifolds},
year={2021},
volume={8},
pages={150 - 182}
}
• Severin Bunk
• Published 1 January 2021
• Mathematics
• Complex Manifolds
Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we…
3 Citations
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## References

SHOWING 1-10 OF 106 REFERENCES

• Mathematics
Communications in Mathematical Physics
• 2021
We study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line
. Just as C × principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral
• Mathematics
• 2013
We consider topological T-duality of torus bundles equipped with S^{1}-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S^{1}-valued functions which
Surface holonomy of connections on abelian gerbes has essentially improved the geometric description of Wess-Zumino-Witten models. The theory of these connections also provides a possibility to
• Mathematics
• 2009
Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing
• Mathematics
• 2016
We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a programme of higher geometric quantisation of closed
We present a construction of a 2-Hilbert space of sections of a bundle gerbe, a suitable candidate for a prequantum 2-Hilbert space in higher geometric quantisation. We introduce a direct sum on the
• Mathematics
• 2012
The theory of principal bundles makes sense in any ∞-topos, such as the ∞-topos of topological, of smooth, or of otherwise geometric ∞-groupoids/∞-stacks, and more generally in slices of these. It
• Mathematics
Differential Geometry and its Applications
• 2022