November 29, 2005

“Area Metric” Manifolds

Posted by Urs Schreiber

David Roberts made me have a look at the recent preprint

F. Schuller & M. Wohlfarth
Canonical differential structure of string backgrounds
hep-th/0511157.

Posted at 2:43 PM UTC | Permalink | Followups (10)

November 22, 2005

Line-2-Bundles and Bundle Gerbes

Posted by Urs Schreiber

I’d be grateful for any comments on the following notes.

Line-2-Bundles and Bundle Gerbes

Abstract:

A line-2-bundle with 2-connection is defined to be a smooth functor from 2-paths to ${\mathrm{Vect}}_{1}$, where ${\mathrm{Vect}}_{1}$ is regarded as a 2-category with a single object. Pre-trivializations of a line-2-bundles are defined and shown to be in bijection with abelian bundle gerbes. The 2-category of pre-trivialized line-2-bundles should be equivalent to that of abelian bundle gerbes over a fixed fibration.

$\phantom{\rule{thinmathspace}{0ex}}$

Posted at 7:59 PM UTC | Permalink | Followups (8)

November 17, 2005

KK Reference

Posted by Robert H.

I am looking for a reference for the fact that it is impossible to get non-abelian gauge groups or chiral fermions by KK-reduction of 11d sugra on a compact 7-manifold without singularities. IIRC this was announced by Witten on a conference long ago but so far I have been unsuccesful to dig up the exact reference. Actually, I am more interested in the argument than the original reference, so any other place that proves this is also welcome. If you know anything about his please leave a comment or send me a mail. Thanks
Posted at 2:13 PM UTC | Permalink | Followups (1)

November 15, 2005

CFT and SLE

Posted by Urs Schreiber

Just heard a talk by Roland Friedrich on stochastic Loewner evolution (SLE) and its relation to CFT. This is the same topic that John Cardy talked about recently under the title a new way of thinking about conformal field theory. Robert had reported some key ideas mentioned in Cardy’s talk here. I want to better understand this stuff. Here are some elementary notes.

The slides of John Cardy’s talk are available online. A useful recent review is

D. Bernard
Conformal Field Theories in Random Domains and Stochastic Loewner Evolutions
hep-th/0309080

Posted at 6:45 PM UTC | Permalink | Followups (6)

November 13, 2005

Lauda & Pfeiffer on Open-Closed Topological Strings

Posted by Urs Schreiber

Here are some notes on the recent preprint

A. Lauda & H. Pfeiffer
Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras
math.AT/0510664

Posted at 2:31 PM UTC | Permalink | Followups (14)

November 9, 2005

Strings on Stacks II

Posted by Urs Schreiber

Here is more on what Eric Sharpe has to say about strings on stacks, continuing the discussion from the previous entry.

Posted at 5:32 PM UTC | Permalink | Followups (2)

November 8, 2005

Strings on Stacks I

Posted by Urs Schreiber

Eric Sharpe is currently visiting our group. Tomorrow he’ll give a talk on

Deformation theory, mirror symmetry, gauging noneffective group actions, and stacks

based on hep-th/0502044 and hep-th/0502053.

(If anyone is close to Hamburg and would like to attend (Robert? :-): it’s 11:30 in room 127 of the ‘Geomatikum’ building.)

Here are some notes on some of the basic ideas concerning strings on stacks.

Update June 6, 2006.

Today a new preprint has appeared with more details on this topic:

S. Hellerman, A. Henriques, T. Pantev, E. Sharpe, M. Ando
Cluster decomposition, T-duality, and gerby CFT’s
hep-th/0606034 .

Posted at 3:43 PM UTC | Permalink | Followups (9)

November 7, 2005

2-Equivariance and “Weak Pullback”

Posted by Urs Schreiber

Here is math question related to strings on orbifolds which I have just submitted to sci.math.research. Replies of all kinds are very welcome.

Posted at 5:41 PM UTC | Permalink | Followups (10)

November 2, 2005

Classical, Canonical, Stringy

Posted by Urs Schreiber

In the last entry the following question was raised (in slightly different formulation):

Classical mechanics of point particles is governed by symplectic geometry and hence in particular by a symplectic 2-form ${\omega }_{2}$. We know that, morally, stringification lifts form degrees by one.

Hence: Is there a V.I. Arnold-like generalization of this which replaces the symplectic 2-form by a three form and describes the dynamics of 1-dimensional objects? If so, how?

(Of course we know how to describe field theory using a symplectic 2-form on an infinite-dimensional space. And the dynamics of a 1-dimensional object is just 1+1 dimensional field theory. Hence whatever answer the above question has, it should be reducible to the ordinary setup.)

You might object that this sounds like a typical excercise for a mathematical physicist who is interested in reformulating something that everybody already understands. But there should be more to it.

Anyway, I think that a very good approach to answering this question has been given a couple of years ago in

C. Rovelli
Covariant hamiltonian formalism for field theory
gr-qc/0207043 .

I’ll try to review some key ideas.

Posted at 6:25 PM UTC | Permalink | Followups (7)

November 1, 2005

Gerbes, strings, and Nambu brackets

Posted by Urs Schreiber

John Baez asks me to forward the following question to the Coffee Table. It’s an intriguing question, related (to my mind at least) to the question how ‘categorified quantum theory’ and string/loop physics are related. But it’s much more concrete than that.

Posted at 1:30 PM UTC | Permalink | Followups (13)