Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM

By F. Cachazo, Song He, E. Y. Yuan. 2014

455 citations recorded by the source corpus.

A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1)M . The second operation turns gravitons into gluons and we call it “squeezing”. This gives rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills. Dimensionally reducing Yang-Mills we find the S-matrix of a special Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of a YMS theory with an additional cubic scalar vertex. A corollary of the YMS formula gives one for a single massless scalar with a ϕ4 interaction. Starting again from Einstein’s theory but in d + d dimensions we introduce a “generalized dimensional reduction” that produces the Born-Infeld theory or a special Galileon theory in d dimensions depending on how it is applied. An extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI) theory. By applying the same operation to Yang-Mills we obtain the U(N ) non-linear sigma model (NLSM). Finally, we show how the Kawai-Lewellen-Tye relations naturally follow from our formulation and provide additional connections among these theories. One such relation constructs DBI from YMS and NLSM.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1c542a5dc28ec9b82d787e65388337f0496297c7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Humberto Gomez
2. Tim Adamo
3. Song He
4. N. Arkani-Hamed
5. Yuntao Bai
6. Gongwang Yan
7. A. Sharma
8. L. Mason

In Nuclear and High Energy Physics

1. C. Cheung
2. N. Arkani-Hamed
3. Tim Adamo
4. Yuntao Bai
5. J. Trnka
6. Humberto Gomez
7. L. Mason
8. Song He

Citations in the corpus

• Scattering forms and the positive geometry of kinematics, color and the worldsheet (2017, methodology): “And of course, these forms are again obtained as the “pushforward” via the scattering equations from the familiar differential forms on the worldsheet [15, 21], in parallel to the bi-adjoint theory.”
• A periodic table of effective field theories (2016, background): “These very same EFTs also appeared in a completely different context from the CHY scattering equations [8], which is a simple construction for building the S-matrices for certain theories of massless particles.”
• Celestial amplitudes and conformal soft theorems (2019, methodology): “CHY formulae for celestial amplitudes The remarkable formulae of Cachazo–He–Yuan (CHY) for tree-level scattering amplitudes in a wide variety of massless QFTs take the universal form [28, 29]:”
• Λ scattering equations (2016, background): “Consider for example the integrands for four particles [2, 3, 11]”
• Unifying relations for scattering amplitudes (2017, methodology): “Note that Lij is equivalent to the “compactify” operation for CHY integrands presented in [5], here generalized to any representation of the amplitude.”
• TASI Lectures on Scattering Amplitudes (2017, background): “A partial explanation can be found in the scattering equations of Cachazo, He, and Yuan [98, 99, 75], who proposed an extraordinarily compact construction for the S-matrices of all the theories in Fig.”