On Transport Theory


Posted by urs


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On Wed., Feb. 22, 18:00 there will be a talk (Hamburg math department)


On Transport Theory


Abstract:




n-transports are an n-functors  
describing 



parallel trasport in n-bundles


propagation in n-dimensional QFT.


We describe basic notions of n-transport theory,
such as trivialization, transition and trace
and discuss examples.


This is a synthesis of the
material contained in 
[I,
II,
III,
IV,
V,
VI].

This looks fascinating. Wish I could be there to hear it. Good luck!


Eric


PS: How far away are you from describing string theory within this framework of transport, i.e. QFT, on loop space (if that was the goal)? :)

Posted by:
Eric on February 17, 2006  6:06 PM | Permalink

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Re: On Transport Theory


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How far away are you from describing string theory within this framework of transport, i.e. QFT, on loop space (if that was the goal)? :)




I am trying to show that certain 2-vector transport (transport with target the 2-category C-Mod of module categories over an abelian monoidal category C) captures topological strings as described by Fukuma-Hosono-Kawai and captures CFT as described by Fuchs-Runkel-Schweigert. This does seem to work, at least concerning some aspects of these formulations.


As I have tried to point out recently, such 2-vector transport can be understood as sort of a categorified QM. In particular, if you restrict attention to the vertical composition of 2-morphisms you do get something like QM on path space from this.


So, I think, yes, this does work. There are however many loose ends that need to be worked out further.