## February 17, 2006

### On Transport Theory

#### Posted by Urs Schreiber

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].

Posted at February 17, 2006 3:18 PM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/753

### 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)? :)

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

### Re: On Transport Theory

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 $C-\mathrm{Mod}$ 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.

Posted by: urs on February 19, 2006 9:54 AM | Permalink | Reply to this
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