A more substantial post is upcoming, but I wanted to get out this announcement for a conference I’m helping to organise, along with Roger Picken, João Faria Martins, and Aleksandr Mikovic. Its website: https://sites.google.com/site/hgtqgr/home has more details, and will have more as we finalise them, but here are some of them:

## Workshop and School on Higher Gauge Theory, TQFT and Quantum Gravity

Lisbon, 10-13 February, 2011 (Workshop), 7-13 February, 2011 (School)

Description from the website:

Higher gauge theory is a fascinating generalization of ordinary abelian and non-abelian gauge theory, involving (at the first level) connection 2-forms, curvature 3-forms and parallel transport along surfaces. This ladder can be continued to connection forms of higher degree and transport along extended objects of the corresponding dimension. On the mathematical side, higher gauge theory is closely tied to higher algebraic structures, such as 2-categories, 2-groups etc., and higher geometrical structures, known as gerbes or n-gerbes with connection. Thus higher gauge theory is an example of the categorification phenomenon which has been very influential in mathematics recently.

There have been a number of suggestions that higher gauge theory could be related to (4D) quantum gravity, e.g. by Baez-Huerta (in the QG^2 Corfu school lectures), and Baez-Baratin-Freidel-Wise in the context of state-sums. A pivotal role is played by TQFTs in these approaches, in particular BF theories and variants thereof, as well as extended TQFTs, constructed from suitable geometric or algebraic data. Another route between higher gauge theory and quantum gravity is via string theory, where higher gauge theory provides a setting for n-form fields, worldsheets for strings and branes, and higher spin structures (i.e. string structures and generalizations, as studied e.g. by Sati-Schreiber-Stasheff). Moving away from point particles to higher-dimensional extended objects is a feature both of loop quantum gravity and string theory, so higher gauge theory should play an important role in both approaches, and may allow us to probe a deeper level of symmetry, going beyond normal gauge symmetry.

Thus the moment seems ripe to bring together a group of researchers who could shed some light on these issues. Apart from the courses and lectures given by the invited speakers, we plan to incorporate discussion sessions in the afternoon throughout the week, for students to ask questions and to stimulate dialogue between participants from different backgrounds.

Provisional list of speakers:

- Paolo Aschieri (Alessandria)
- Benjamin Bahr (Cambridge)
- Aristide Baratin (Paris-Orsay)
- John Barrett (Nottingham)
- Rafael Diaz (Bogotá)
- Bianca Dittrich (Potsdam)
- Laurent Freidel (Perimeter)
- John Huerta (California)
- Branislav Jurco (Prague)
- Thomas Krajewski (Marseille)
- Tim Porter (Bangor)
- Hisham Sati (Maryland)
- Christopher Schommer-Pries (MIT)
- Urs Schreiber (Utrecht)
- Jamie Vicary (Oxford)
- Konrad Waldorf (Regensburg)
- Derek Wise (Erlangen)
- Christoph Wockel (Hamburg)

The workshop portion will have talks by the speakers above (those who can make it), and any contributed talks. The “school” portion is, roughly, aimed at graduate students in a field related to the topics, but not necessarily directly in them. You don’t need to be a student to attend the school, of course, but they are the target audience. The only course that has been officially announced so far will be given by Christopher Schommer-Pries, on TQFT. We hope/expect to also have minicourses on Higher Gauge Theory, and Quantum Gravity as well, but details aren’t settled yet.

If you’re interested, the deadline to register is Jan 8 (hence the rush to announce). Some funding is available for those who need it.

December 15, 2010 at 8:39 pm

Well, I see they have a token female in there. It’s a very loopy crowd, which I guess goes with the conference theme, but is a bit odd given the interests of some of the mathematicians.

December 16, 2010 at 12:35 am

The list of invited speakers is a bit idiosyncratic, in that a fair proportion consists of people the various organizers knew, who were interested in the main topics. If idiosyncratic has translated to lopsided, hopefully there will be enough time for people to find out and offer some contributed talks too…

December 17, 2010 at 7:21 am

I think it’s good that you’re inviting people on both the quantum gravity and the higher category side of things. Ever since Louis Crane invention of the term ‘categorification’, the dream was that these should be related somehow. It still hasn’t quite gelled, but especially now that we know superstring and super-2-brane theories can be seen as 2-supergroups and 3-supergroup gauge theories, it seems that categorification is something everyone who wants to quantize gravity should learn about. Maybe someday it’ll really pay off.

December 17, 2010 at 1:24 pm

Yes – it seems that higher gauge theory is the thing (or

athing) that is bringing those two sides together, at least in this case. It’s also nice, from a physics point of view, that by starting with gauge theory, it can be relevant to both loopy and stringy technology. The middle term of the title, TQFT, is supposed to help bridge the gap a bit, since it can be viewed from the physics end or the categorical end. There seems to be some big story here that hopefully will become clearer after putting these folks in the same place for a while…December 18, 2010 at 2:01 am

I’m certainly looking forward to this event!

December 18, 2010 at 4:18 am

Hi Chris! Yes, so am I. Your course for the school part should be interesting. I’ve just been revising a paper mostly on 3D ETQFT, and it’ll be nice to see the 2D world in some depth.

I point other readers at Chris’ website, since I gather the course should cover a lot of stuff from his dissertation, which is there, and gives a classification for 2D Extended TQFT’s. Though I notice there’s also some new stuff about 2-groups, which I hadn’t known until now.

December 18, 2010 at 5:32 pm

Yes the 2-group stuff is pretty fun. I just posted a new version of my central extension/String group paper to the ArXiv.

I’m interested to hear about your 3D work. I have a couple 3D projects which are finally bearing fruit.

December 17, 2010 at 9:08 pm

Oh, come on. In 2010 there is no excuse for holding such a conference with only loopies and stringers on the ‘physics’ side. What about quantum information, condensed matter and many other fields that now use categorical techniques? These fields have just as much insight into quantum gravity (in fact, more) as the traditional QG camps.

December 18, 2010 at 1:50 am

Well, the unifying theme here is higher gauge theory, and in particular applications in physics. If those areas make use of it, it would be great to have speakers on them. I suppose TQFT does have some overlap with quantum information (Frobenius algebras and observable structures, e.g.) but I’m not familiar with applications of HGT in those areas. The overlap with QG and information is definitely interesting. I don’t know much about the overlap with condensed matter – perhaps HGT appears in there somewhere…

December 18, 2010 at 4:07 am

The loopy definition is too restrictive. The term ‘higher gauge theory’ should refer to any use of higher dimensional category theory in QFT related physics. This would include Wen’s string nets, extended TFTs, some NCG ideas, just to name a few.

December 18, 2010 at 4:29 am

Well, we are certainly having some talk about extended TFT’s (see the above comment by Chris Schommer-Pries). So far I haven’t seen anyone wanting to talk about NCG or string nets. I don’t know much about string nets, though a cursory search suggests to me that you’re right that there is interesting stuff there. I do know a little more about the NCG ideas you may mean – Marcolli has a bunch of recent work that seems to qualify, say). This particular workshop is of a size where it needs to focus a bit more narrowly.

I think it will be great when someone puts together a conference that can address all those different uses of n-cats in QFT. As to whether all such uses should be called Higher Gauge Theory – all I can say is that here it’s being used in a fairly standard way, where we’re talking about connections based on categorical groups as gauge groups (and higher variants thereof).

December 18, 2010 at 5:07 am

Well, the main problem with the narrow definition is that it has nothing directly to do with real physics. But as a conference on mathematical techniques it looks interesting. Of course I am still living in poverty in the antipodes, so I will not be going, but then I wasn’t welcome anyway.

December 18, 2010 at 2:37 pm

I don’t know why you’d think you weren’t welcome, but for sure it’s a long way to come.

As you say, though, this is a workshop on certain mathematical methods, which look potentially promising for, but haven’t yet become mainstream in, real physics (which is to say, physics that can be experimentally tested). Trying to make that contact is one reason for this particular workshop.

December 18, 2010 at 7:42 pm

Really? You want to make some contact with experiment? Well, then you really should have invited me.

December 18, 2010 at 7:42 pm

[...] is the conference website, and a blog post by one of the [...]

December 18, 2010 at 11:17 pm

If I may elaborate a little further. To a mathematician interested in higher dimensional category theory and QFT, such as the interesting arithmetic structures studied by Marcolli et al in NCG, there may not be much difference between the physics of NCG and that advocated by the same mathematics within string theory. This is the impression one often gets from what is said. For a physicist, however, there is a WHOLE WORLD of difference between (i) advocating SUSY partners or not (ii) advocating God particles or not (iii) advocating a WIMP form of dark matter or not … and so on.

This needs to be better appreciated by your community (of which I am clearly not a part). In fact, if we draw up a physics score card for stringers, loopies, NCGers and so on … I am clearly now leading the table. So I figure I am entitled to an opinion.

December 19, 2010 at 10:59 pm

I agree with your opinion that those kind of distinctions need to be better appreciated in the mathematical community. I do think it’s understandable that they’re not really taken to heart, by people (including me, for sure) who work toward the beginning of the chain: (1) develop mathematical tools for building theories; (2) use the tools to construct a theory or class of physical theories; (3) perform calculations using the theories to make predictions; (4) devise and perform experiments to test predictions. I, and most of the organizers, I think, tend to work mainly on step (1), and to some extent on step (2), though even there there’s a lot of working with toy models to give feedback to step (1). The interest in physics is mainly about interacting with people bridging the gap between steps (2) and (3) in a similar way, though when the physics is “quantum gravity” my impression is that (3) is presenting lots of challenges and (4) is at present fairly intractable except maybe for some cosmological observations.

As for invitations: for budget reasons, as you may observe, the majority of invitees are within the EU, and we expect most attendees will be as well, though a few North Americans with specific connections to the named topics have also been invited. OTOH it’s not an invitation-only event, which is why it’s being announced.

December 20, 2010 at 12:57 am

Mathematicians appear to be fond of this idea, but Theoretical Physics does not follow the program 1,2,3,4. No progress has ever been made in Physics without a thorough feeling for the experimental state of affairs, in particle physics, cosmology and more. At this point people often pull out GR as a top down example, but they only demonstrate their ignorance of its rich experimental and philosophical history.

December 20, 2010 at 1:49 am

I certainly don’t mean to imply that the links in that chain occur in chronological order. On the contrary, the links adjacent to one have an influence in either direction. The tools of (1) are developed in response to the needs of the theories that use them at (2), as well as according to their internal logic, which gives new information back to (2), and so on. Likewise, the theories try to account for evidence, which informs what they’re supposed to be doing. New theories then influence how evidence is interpreted and collected. Influence back and forth is supposed to be happening all the time. When it’s not, any of those areas can produce new material rapidly, but it’s not likely to make much “progress”. But they are conceptually different kinds of activity. Anyone who can work on all four kinds is very impressive to someone like me, a mere mathematician interested in physics.

December 20, 2010 at 2:03 am

Influence back and forth is supposed to be happening all the time.Indeed. But it ain’t. I’ve been doing this for decades now, and all I see around me is a bunch of arrogant idiots who don’t have a clue about anything outside their own narrow speciality, which keeps them safe and cosy in their neat little world. Well, good luck with the conference, but if you think the only progress that has been made is in cosmology … you need to get out more.