## April 21, 2011

### Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

#### Posted by Urs Schreiber

In May there is the following workshop in Cardiff:

• Workshop on Higher Gauge Theory, TQFT and Categorification

Monday 9th - Tuesday 10th May 2011

School of Mathematics, Cardiff University

website

organized by WIMCS, more precisely by the Mathematical Physics Cluster of the Wales Institute of Mathematical and Computational Sciences. Timothy Porter is doing the organisation of the programme whilst the hard work is being done by Mathew Pugh and David Evans down in Cardiff.

Below are some of the speakers, talk titles and abstracts. The list is incomplete. If you are a speaker and would like more information about your talk be visible here, please send me an email.

• Aristide Baratin (Orsay, Paris)

State sum invariant from a 2-category

Abstract: ‘State sum models’ are discrete functional path integrals. Using the combinatorics of the Pachner moves of the triangulation to convert a topological problem into an algebraic one, these models can be used to define manifold invariants and topological quantum field theories. Just as 3d state sum models can be built using categories of group representations, 2-categories of 2-group representations may provide interesting state sum models for 4d quantum topology, if not quantum gravity. I will describe the construction of the first non-trivial example of a such models, based on the representations of the ‘Euclidean 2-group’, built from the rotation group SO(4) and its action on the translation group of Euclidean space. I will show that this model gives a new way to compute Feynman integrals for ordinary quantum field theories on 4d Euclidean spacetime.

• Benjamin Bahr (Cambridge)

State-sum models and coarse graining in quantum gravity

Abstract: In this talk a general framework will be reviewed, in which to formulate physical theories discretized on two-complexes, being closely related to manifold invariants constructed from TQFTs. Examples for such theories are Lattice gauge theories, Ising spin systems, and in particular the Spin Foam approach to quantum gravity. In the rest of the talk, the problem of finding a continuum limit for the discretized theories is discussed, and it is shown how this is related to constructing triangulation-independent state-sum models, and renormalization in statistical field theories.

• Jeffrey Giansiracusa (Bath)

Topological field theory and deformation theory

Abstract: This is a speculative talk about some very early stage research in progress. Costello proved that an open string topological conformal field theory is essentially the same as an $A_\infty$ algebra, and that an open TCFT has a universal closed counterpart that is closely related to the deformation theory of the open part. Recently B. Cooper found a $C_\infty$ analogue of Costello’s theorems. I’ll discuss these theorems and how they points towards the possibility of a generalized Deligne Conjecture that would construct from any (cyclic or modular) operad $P$ the universal algebraic structure acting on the deformation theory of $P$-algebras.

• Alexander Kahle (Göttingen)

Higher Abelian Gauge Theory and Differential Cohomology

Abstract: In this talk I will describe how the subject of differential cohomology gives a useful framework for discussing higher gauge theory, and is in some sense necessitated by Dirac charge quantisation. The talk will be example driven, and I hope to discuss ordinary and higher Maxwell theory, as well as some of the theory of Ramond-Ramond fields and D-Branes, and how (twisted) K-theory enters the picture there. Time permitting, I will mention some recent work with Alessandro Valentino investigating T-Duality in this context.

• Jeffrey Morton (Lisbon)

ETQFT by Induced Representations

Abstract: Extended topological quantum field theory (ETQFT) is the categorification of ordinary TQFT, described in terms of a 2-functor from a cobordism category into 2-vector spaces. I describe how a class of such ETQFT’s can be given, one for any finite group G, via gauge theory. This uses a universal construction a category of groupoids and spans, through the adjunction between restriction and induction of representations. I will describe this construction and sketch the generalization to (compact) Lie groups.

• Urs Schreiber (Utrecht)

$\infty$-Connections and their Chern-Simons functionals

Abstract: I indicate a general theory of higher gauge fields/higher connections and how they naturally come with their higher Chern-Simons functionals / Chern-Weil homomorphisms. Then I demonstrate some applications to supergravity, such as the description of the Green-Schwarz mechanism by twisted differential string structures.

(aspects of chapter 4 of differential cohomology in a cohesive topos)

• Jamie Vicary (Oxford)

123 TQFTs

Abstract: Abstract: I will present some new results on classifying 123 TQFTs, using a 2-categorical approach. The invariants defined by a TQFT are described using a new graphical calculus, which makes them easier to define and to work with. Some new and interesting physical phenomena are brought out by this perspective, which we investigate. I will finish by banishing some TQFT myths! This talk is based on joint work with Bruce Bartlett, Chris Schommer-Pries and Chris Douglas.

Geometric string structures and supersymmetric sigma models

Abstract: I describe a simple, finite-dimensional definition of geometric string structures, equivalent to the ones of Stolz and Teichner. Geometric string structures play an important role for the path integral quantization of supersymmetric sigma models, and I try to explain this using recent work of Bunke and a new transgression formula for 2-gerbes.

• Christoph Wockel (Hamburg)

A smooth model for the string group

Abstract: There have been various constructions of the string group out that are suited for differential geometric applications. It cannot be a finite-dimensional Lie group, so one of the most natural things to expect would be an infinite-dimensional Lie group. Surprisingly, such a model did not exist in the past. In this talk we explain how to construct such a model, based on the construction of a topological model by Stolz. Moreover, we show how this can be extended to a Lie 2-group model, making explicit comparisons between ordinary and categorical differential geometry possible.

Posted at April 21, 2011 9:25 AM UTC

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### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

Jeffrey Giansiracusa (Bath)

Open closed field theories and deformation theory

his page or even just his e-address?

Posted by: jim stasheff on April 21, 2011 1:14 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

There are webpages for Jeff at Bath, Swansea and Oxford!

This is one of them

http://people.bath.ac.uk/jg479/

Posted by: Tim Porter on April 21, 2011 4:49 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

and I see that the Oxford one is now linked to the café entry.

Posted by: Tim Porter on April 21, 2011 4:51 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

Right, now all speaker names have been hyperlinked.

Posted by: Urs Schreiber on April 21, 2011 4:51 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

I should have mentioned that this short meeting is organised by WIMCS, more precisely by the Mathematical Physics Cluster of the Wales Institute of Mathematical and Computational Sciences. I am doing the organisation of the programme whilst the hard work is being done by Mathew Pugh and David Evans down in Cardiff.

Posted by: Tim Porter on April 22, 2011 6:38 AM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

I have now added in the titles and abstracts for the talks by Jeffrey Giansiracusa, Jamie Vicary and Konrad Waldorf (kindly provided by Tim Porter).

(I have also added the details on the conference organization responsibilities, as mentioned by Tim.)

Posted by: Urs Schreiber on April 23, 2011 10:52 AM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

Konrad and I will meet at 7pm local time down in the lobby of Parc Hotel in order to join forces to find some dinner. Anyone reading this here and also based in Parc Hotel or vicinity, feel invited to join us!

Posted by: Urs Schreiber on May 8, 2011 6:08 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

I made some “introductory and survey”-notes on $\infty$-Chern-Simons theory . Here.

Posted by: Urs Schreiber on May 9, 2011 1:04 PM | Permalink | Reply to this

### Re: Workshop on Higher Gauge Theory, TQFT and Categorification in Cardiff

Konrad Waldorf in his talk reviewed the recent rigorous version by Uli Bunke of the old argument by Killingback of the quantum anomaly cancellation on the worldsheet for the heterotic superstring, coming from a string structure on the target.

I used the occasion to start an entry fermionic path integral . This is now effectively 2/3rds of the notes of Konrad’s talks. He proceeded with discussion as can be seen at differential string structure .

Have to run now to the next talk…

Posted by: Urs Schreiber on May 10, 2011 2:57 PM | Permalink | Reply to this

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