nLab
fusion bundle
Contents
Context
Bundles
bundles

covering space

retractive space

fiber bundle , fiber ∞-bundle

numerable bundle

principal bundle , principal ∞-bundle

associated bundle , associated ∞-bundle

vector bundle , 2-vector bundle , (∞,1)-vector bundle

real , complex /holomorphic , quaternionic

topological , differentiable , algebraic

with connection

bundle of spectra

natural bundle

equivariant bundle

Contents
Idea
The image of the transgression operation from bundle gerbes (with connection ) to complex line bundles (with connection ) on the free loop space of their base space may be characterized (Waldorf 2009 , 2010 , 2011 ) as consisting of bundles which are suitably compatible with the “fusion” of pairs of loops along thin trinions .

Definition
(…)

Properties
General properties
(…)

Relation to string field theory?
Curiously, the fusion operation that is formalized by the notion of fusion bundles is mathematically reminiscent of (and physically of essentially the same intuitive nature as) the “star product” on closed string fields considered in string field theory [Witten (1986),Fig. 20 ]:

References
Konrad Waldorf , Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps , Cah. Topol. Geom. Differ. Categ., 2012, Vol. LIII, 162-210 [arXiv:0911.3212 , cahierstgdc:LIII ]

Konrad Waldorf , Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection , Asian Journal of Mathematics 20 1 (2016) 59-116 [arXiv:1004.0031 , doi:10.4310/AJM.2016.v20.n1.a4 ]

Konrad Waldorf , Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles , Advances in Mathematics 231 (2012) 3445-3472 [arXiv:1109.0480 , doi:10.1016/j.aim.2012.08.016 ]

Last revised on April 17, 2023 at 11:01:59.
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