On Wed., Feb. 22, 18:00 there will be a talk (Hamburg math department)
Abstract:
Posted at February 17, 2006 3:18 PM UTC-transports are an -functors describing
parallel trasport in -bundles
propagation in -dimensional QFT.We describe basic notions of -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].
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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 of module categories over an abelian monoidal category ) 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.
Re: On Transport Theory
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)? :)