I spent yesterday up in Providence, visiting the Theoretical Physics Center at Brown, and giving a talk there (slides are available here, newer version of a paper here), At some point a recording of the talk should appear online. In the talk I tried to emphasize some basic things which it took me a very long time to appreciate:
- The ways in which Euclidean QFT is very different than Minkowski space-time QFT, in particular the necessity of having a distinguished imaginary time vector, breaking SO(4) invariance, in order to recover Lorentz (SL(2,C)) invariance.
- The way in which Minkowski space-time shows up when you do twistor theory in Euclidean space-time (see the pictures in the slides). This again makes clear the way SO(4) invariance is broken.
While I’m making a proposal for how to get gravity out of chiral 4d geometry, I’ve never been that expert in GR, and GR is the focus of much of the theory community these days, in particular the theorists at Brown. So, they had lots of questions about what the implications of this are for GR that I couldn’t answer. I’ll keep thinking more about this and may some day start to have answers (or maybe GR experts will find this proposal interesting enough to figure out the answers themselves).
I was invited to give the talk by Stephon Alexander, and got to spend some time talking with him while in Providence. He has worked in the past (see here) on ideas that bring together the gravitational and weak interactions in a similar way. More recently he has been working on ideas for how one might observe an unexpected chiral component to the gravitational interactions, and now has a grant from the Simons Foundation that will fund work in this area. Next week he’ll be here at Columbia giving an astronomy colloquium on the topic.
He also has a new book (his first was The Jazz of Physics) out, Fear of a Black Universe: an Outsider’s Guide to the Future of Physics. It’s quite interesting, with much of the earlier parts describing some of his experiences making a career for himself as a theorist, together with explanations of the physics background. The last part (in collaboration with Jaron Lanier) heads off in somewhat of a sci-fi direction, an excerpt is here.
A major theme of the book (with which I’m very sympathetic) is that the community doing this sort of theoretical physics desperately needs to get out of its current rut and open itself to new ideas, which often will come from “outsiders”. One aspect of being an “outsider” that Alexander has experienced is difference in racial background, but he’s concerned with a more general context of hostility to ideas that aren’t those currently favored by “insiders”. While he started out his career doing string theory, he has moved in different directions over the years. He explains that as a postdoc at SLAC he invited Lee Smolin to come and lecture on loop quantum gravity, something which was not at all well received by the local string theorists. While I’m quite interested for my own reasons to understand better what he has been doing with the physics of possible chiral effects in gravity, it was great to see his enthusiasm for and encouragement of ideas that don’t fit exactly into the narrow conception of the subject that now dominates all too much of the community doing fundamental theoretical physics.
Update: There’s video of the talk available here.
What about Yukawa couplings? Attempts to find simplicity behind the Higgs usually sink when dealing with the fact that the SM Higgs has Yukawa couplings with messy values.
No idea how to compute Yukawa couplings. Part of that problem is not understanding where three generations come from.
Whenever I see phrasing about a chiral component to gravity, I get flashbacks to noted physics Internet personality Uncle Al, and his claims that “someone should look” to see if left-handed chiral crystals and right-handed chiral crystals obey the equivalence principle.
Have you contemplated the possibility that, from the viewpoint of a QFT formulated in the standard spacetime language, the action functional corresponding to the gravitational theory following from your proposal of symmetry breaking leading from Euclidean to Lorentzian signature, would include terms that might involve metric-affine geometry (Cartan connection), e.g., torsion, instead of the standard Levi-Civita connection? Or more generically a Ehresmann connection?
Might be worth looking for a debate between Weinberg and Hehl on the merits of such geometries, if this turns out to be relevant to what you are up to.
There are various ways to extend GR formulated with a spin connections and the Palatini action:
1. Allow torsion
2. What I’d call Cartan geometry, interpreting the vierbeins as a Cartan connection. One version of this is Macdowell-Mansouri.
3. Add R^2 terms, get a conformally invariant theory, I noticed there was a paper about this on the arxiv yesterday:
All of these have a long history, perhaps reformulating in the twistor Euclidean framework with the imaginary time direction vierbein getting the dynamics of the Higgs gives something new.
Long time lurker here. This twistor gravi-weak unification is really awesome and the way in which the Higgs emerges due to Osterwalder – Schrader reflection is very very deep.
Couple of basic questions (I dont know if you have addressed these already):
1) Where do three generations come from?
2) How does QCD fit into this framework?
3) Do you have any comment on what objects of algebraic quantum field theory like the modular operator look like in this framework?
Thanks for your comments about the unification and Higgs ideas. The more I think about these ideas the more convinced I become that something like this can work. Also, the more I look at the literature, the more convinced I become that these ideas are actually new.
1. I don’t understand the origin of three generations, understanding that is crucial. There are various possible ideas to look at that I haven’t yet had time to pursue.
2. The definition of projective twistor space naturally provides an internal SU(3) symmetry, one can try and gauge this, use the usual Yang-Mills action, get standard QCD. There is however something different going on: the SU(3) principal bundle on projective twistor space is not the pull-back of an SU(3) principal bundle on the base space-time. The SU(3) group varies as you move around the CP1 fiber. I need to better understand the significance of this, how and if it changes the usual QCD dynamics.
3. I know precious little about algebraic qft.