Exploring the Progress and Challenges of Twistor Theory in Quantum Gravity

[tom.stoer]

Are there any news regarding twistor theory?

The original ideas by Penrose to replace spacetime by its "dual lightcones" always fascinated me, but it seems the whole program is stuck. What are the reasons? Is there any progress and relation to recent progress in other QG approaches?

Tom

 

[yenchin]

There are works in progress... although I don't know much about the details, but take a look at
http://www.twistordiagrams.org.uk/

See also the talk by Nima Arkani-Hamed.

http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=ff8f97a4-2848-4b93-98d9-1218de2070af&shouldResize=False

 

[atyy]

http://online.kitp.ucsb.edu/online/qcdscat11/

http://pirsa.org/C10018

A quick summary is found in the first few pages of Bourjaily's thesis.
http://www.princeton.edu/physics/academics/graduate-program/theses/theses-from-2011-1/bourjaily_princeton_thesis.pdf

 

[tom.stoer]

All these papers focus on scattering amplitudes; is twistor theory as of today "only" a calculational tool, or is there some fundamental light-cone structure replacing spacetime? Has Penrose's original program suceeded or failed?

 

[atyy]

All these papers focus on scattering amplitudes; is twistor theory as of today "only" a calculational tool, or is there some fundamental light-cone structure replacing spacetime? Has Penrose's original program suceeded or failed?

I don't think that's known. The hope is that it is the "magic" underlying AdS/CFT and points to more general non-perturbative formulation of string theory. But perhaps it is just a very neat trick for a very specific set of QFTs.

 

[tom.stoer]

I was really interested in the core twistor program.

 

[sheaf]

I was really interested in the core twistor program.

So was I. I worked on the "original" twistor programme, but left to join industry in 1984 and haven't really kept up to date, and my memory's a little hazy. The two main classes of problem I was aware of then were:

1 Twistor theory was good at modelling self-dual or anti self-dual solutions of various physical systems. So, for example, there was a natural way to get, say, anti self-dual solutions from holomorphic functions on twistor space, but no natural way to get the self-dual solutions from holomorphic functions (the "googly problem").

2 It was good for modelling conformally invariant systems, but not for field equations containing mass terms.

 

[qsa]

I was really interested in the core twistor program.

lets see if this could be interresting to you. I am sure you know why I think twister will be the ultimate theory.



http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.0274v2.pdf




This is an elementary and self–contained review of twistor theory as a geometric tool for solving non-linear differential equations...

and ultimately to Einstein–Weyl curved geometries generalising the flat Minkowski space.

 

[Orbb]

You might want to check out

http://arxiv.org/abs/1006.0199

and references therein. It's about the relation of twistor geometry to the classical phase space of loop gravity.

 

[qsa]

check out this thread

https://www.physicsforums.com/showthread.php?t=490749