TL;DR: you can make a lot of maps between physically unrealistic theories. There are hopes that in one of these mappings, scattering might be easier to compute, or at least easier to comprehend. If this works, there are further hopes that it can be generalized to actual physical theories.
First, the summary begins by summarizing some dualities- If you take a toy-model of particle physics with a whole lot of symmetries (super-symmetric Yang-Mills theory) but in 3+1 dimensions you can play some mathematical games. It turns out super-symmetric Yang Mills without gravity is equivalent to a different 5 dimensional theory WITH gravity (a type of string theory).
Similarly, there is a duality between some “simplified” string theories (of a different type) and twistor theory (Twistor theory maps the geometric objects in Minkowski space on to different geometric objects in ‘twistor space’, which is a space with a metric with a (2,2) signature).
Finally, the recent paper proposes a new dual structure, which like twistor theory maps the geometric objects in Minkowski space onto another sort of space. In this new space scattering events can be described by polytopes.
Of course, this is all probably worthless to phenomenologists and theorists who actually want to predict the results of particle experiments- super-symmetric yang mills theory doesn’t describe any actual physical system.
The twistor string gave rise to “BCFW recursion relations” for gauge theories that are now the basis of many practical calculations, notably to model QCD processes at the LHC, the background against which anything new will be detected.
The Grassmannian reformulation of gauge theory in the new paper is a continuation of that research program, and the authors expect it to be generally valid—see page 137, third paragraph.
The only calculations I’ve seen referenced in actual releases from the LHC are either parton-shower calculated backgrounds (pythia), leading-order background (Madgraph,CalcHEP), or at most NLO (MCFM, etc). The automated NLO stuff will probably be soon done with BlackHat, which uses the standard unitarity method that Dixon and Kosower came up with to do the loops. So as far as experiments go, the BCFW relations aren’t really used to do QCD backgrounds. Please point me to a reference, if I’ve missed it.
I left physics for greener pastures after my postdoc and have been working as a statistician for a few years now, but certainly in the first several years of the BCFW recursions, people weren’t doing that much with them. A few fun results for pure gluon amplitudes that were difficult to integrate into the messy world of higher-order QCD calculations (how do you consistently parton-shower when your gluon processes are at all order, and your quark processes are at NLO?), and that was about it.
The most practical use of BCFW that I have found is in arxiv:1010.3991; if you read pages 3 and 4 closely, you’ll see that BCFW was used to construct N=4 amplitudes which were then transposed to QCD and used to calculate a “W + 4 jets” background. I take your point that, although there are theorists using BCFW to model LHC physics, including some from BlackHat, the LHC teams themselves still do their in-house calculations using other methods. Though I think of unitarity cuts as another part of the same big transformation as BCFW.
An article about the underlying math with a very accessible introduction (using lots of illustrative graphs) can be found on Arxiv: ”Scattering Amplitudes and the Positive Grassmannian” by N. Arkani-Hameda
at al http://arxiv.org/pdf/1212.5605v1.pdf
Hmm, I wish someone would summarize this summary in a language accessible to a Physics PhD in an area other than the String Theory.
TL;DR: you can make a lot of maps between physically unrealistic theories. There are hopes that in one of these mappings, scattering might be easier to compute, or at least easier to comprehend. If this works, there are further hopes that it can be generalized to actual physical theories.
First, the summary begins by summarizing some dualities- If you take a toy-model of particle physics with a whole lot of symmetries (super-symmetric Yang-Mills theory) but in 3+1 dimensions you can play some mathematical games. It turns out super-symmetric Yang Mills without gravity is equivalent to a different 5 dimensional theory WITH gravity (a type of string theory).
Similarly, there is a duality between some “simplified” string theories (of a different type) and twistor theory (Twistor theory maps the geometric objects in Minkowski space on to different geometric objects in ‘twistor space’, which is a space with a metric with a (2,2) signature).
Finally, the recent paper proposes a new dual structure, which like twistor theory maps the geometric objects in Minkowski space onto another sort of space. In this new space scattering events can be described by polytopes.
Of course, this is all probably worthless to phenomenologists and theorists who actually want to predict the results of particle experiments- super-symmetric yang mills theory doesn’t describe any actual physical system.
The twistor string gave rise to “BCFW recursion relations” for gauge theories that are now the basis of many practical calculations, notably to model QCD processes at the LHC, the background against which anything new will be detected.
The Grassmannian reformulation of gauge theory in the new paper is a continuation of that research program, and the authors expect it to be generally valid—see page 137, third paragraph.
The only calculations I’ve seen referenced in actual releases from the LHC are either parton-shower calculated backgrounds (pythia), leading-order background (Madgraph,CalcHEP), or at most NLO (MCFM, etc). The automated NLO stuff will probably be soon done with BlackHat, which uses the standard unitarity method that Dixon and Kosower came up with to do the loops. So as far as experiments go, the BCFW relations aren’t really used to do QCD backgrounds. Please point me to a reference, if I’ve missed it.
I left physics for greener pastures after my postdoc and have been working as a statistician for a few years now, but certainly in the first several years of the BCFW recursions, people weren’t doing that much with them. A few fun results for pure gluon amplitudes that were difficult to integrate into the messy world of higher-order QCD calculations (how do you consistently parton-shower when your gluon processes are at all order, and your quark processes are at NLO?), and that was about it.
The most practical use of BCFW that I have found is in arxiv:1010.3991; if you read pages 3 and 4 closely, you’ll see that BCFW was used to construct N=4 amplitudes which were then transposed to QCD and used to calculate a “W + 4 jets” background. I take your point that, although there are theorists using BCFW to model LHC physics, including some from BlackHat, the LHC teams themselves still do their in-house calculations using other methods. Though I think of unitarity cuts as another part of the same big transformation as BCFW.
An article about the underlying math with a very accessible introduction (using lots of illustrative graphs) can be found on Arxiv:
”Scattering Amplitudes and the Positive Grassmannian” by N. Arkani-Hameda at al http://arxiv.org/pdf/1212.5605v1.pdf