Talks at Oxford & Cambridge

In the past couple of days I have been visiting Oxford and then Cambridge, during which I gave one seminar in each place, and an extra talk in an informal journal club in Oxford which was meant to be a pedagogical introduction to the formulation of tree-level amplitudes based on scattering equations. Both seminar talks focus on our recent two papers (arXiv:1409.8256, arXiv:1412.3479) which extended the application of the above mentioned formulation to various theories of massless particles.

Some highlights are that, starting with only two very simple objects (functions of kinematics data and a set of variables parametrizing an auxiliary Riemann sphere with marked points) together with three operations on them, we managed to find out closed formulas for amplitudes in Yang-Mills coupled to gravity (including the well-studied pure gluon amplitudes and pure graviton amplitudes), Einstein-Maxwell, Dirac-Born-Infeld, U(N) non-linear sigma model, and a very special type of the Galileon theory. Furthermore, these new formulas indicates very amusing similarity and connections among amplitudes in these different theories, some of them relatively well-understood from the normal point of view from Kaluza-Klein while others remaining more or less unclear (as of the current status).

The slides for the Oxford talk can be found here.

Due to some change of plan, I switched to a blackboard talk in Cambridge. Most of the contents are similar to that in Oxford, except for a slightly extended review on the general formulation, which can be found here.

In the same file, there is also an additional page related to an update on the Galileon theory that I discussed in the Cambridge talk. In short, the Galileon theory that we identified with one of the new formulas turns out to be a special class of Galileon theories that possess an enhanced symmetry. More discussions on these can be found in paper by Hinterbichler and Joyce (arXiv:1501.07600) late last week.

Soft Limits and Factorizations of the Pfaffian Formula

Very recently F. Cachazo, S. He and I have proposed a new formula (arXiv:1307.2199) for the complete tree-level S-matrix of Yang-Mills and gravity in any dimension, which is based on an integration of the Pfaffian of a skew-symmetric matrix depending on momentum and polarization vectors, over the moduli space of n punctures on a Riemann sphere.

This post is to supplement the paper by providing a detailed proof that our formula satisfies correct soft limits and factorizations both for gluons and gravitons, the most up-to-date notes of which can be found in the following link:

Scattering of Massless Particles in Arbitrary Dimension: Soft Limits and Factorization, v2

Notice: Any comments and remarks are welcome, either by sending us e-mails (preferred) or replying directly to this post. The document here will be updated if we have a better version in future.   — Freddy, Song and Ellis.

Updates in Version 2:

  1. Minor mistakes corrected;
  2. A slightly different convention for the formula has been chosen (which however agrees with that in our previous work arXiv:1306.6575), so that it exactly matches the results from the standard spin-helicity formalism when restricting to 4-dimensions;
  3. Detailed discussions on the behavior of the integration measure by Faddeev-Popov method has been added.

Previous versions can still be found here:

Scattering of Massless Particles in Arbitrary Dimension: Soft Limits and Factorization, v1

Last updated on: 29/08/2013.


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