## 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.

## 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.

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

## November 17, 2005

### KK Reference

#### Posted by Robert H.

## 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

## 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

## 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.

## 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 .

## 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.

## 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.

## 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.