Consistency Conditions on the S-Matrix of Massless Particles

By Paolo Benincasa, F. Cachazo. 2007

241 citations recorded by the source corpus.

We introduce a set of consistency conditions on the S-matrix of theories of massless particles of arbitrary spin in four-dimensional Minkowski space-time. We find that in most cases the constraints, derived from the conditions, can only be satisfied if the S-matrix is trivial. Our conditions apply to theories where four-particle scattering amplitudes can be obtained from three-particle ones via a recent technique called BCFW construction. We call theories in this class constructible. We propose a program for performing a systematic search of constructible theories that can have non-trivial S-matrices. As illustrations, we provide simple proofs of already known facts like the impossibility of spin $s > 2$ non-trivial S-matrices, the impossibility of several spin 2 interacting particles and the uniqueness of a theory with spin 2 and spin 3/2 particles.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d892b94c75bac677e734ffcd9b1c2b06dad4288

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Citations in the corpus

The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “In flat space, the requirement of local four-point interactions is a powerful constraint on the space of consistent interactions between massless particles with spin [86, 87], making almost all theories, other than the familiar gauge theories and gravity, inconsistent.”
The simplest massive S-matrix: from minimal coupling to black holes (2018, background): “ s=m2 = h3jp 1j2]2 u m2 h43i[12] + h13i[42] h3jp 1j2] ! s (5.11) We rewrite the term in the parenthesis, which is simply h1jPj4], as h1jPj4] = 1 2 [14] m + h42i[21] h 12i[24] 2m2 ! + 1 2 h14i m + h13i[34] h 43i[31] 2m2 ! + th34i[21] 2m2h3jp 1j2] 1 2 (F+ F~) + BF+ B (5.12) where Fis written in a way”
A periodic table of effective field theories (2016, methodology): “rivial. In the following, we study this cancellation and use it to derive a no-go theorem for the existence of super-enhanced theories. Our approach mirrors the so-called \four-particle test" of [53] (and see also [54]), where the consistency of higher spin theories was similarly studied via on”
On graviton non-gaussianities during inflation (2011, background): “of the gravitational waves and their momenta, [9](5).”
Scattering Amplitudes and the Positive Grassmannian (2012, background): “[69]) require that any such prefactor must be fully antisymmetric and satisfy a Jacobi identity—implying that color labels combine to form the adjoint representation of a Lie algebra.”
How higher-spin gravity surpasses the spin-two barrier (2010, methodology): “We wish to stress that the Fronsdal programme is based on a working hypothesis: that standard canonical quantization of free fields in ordinary spacetime is actually compatible with the presence of (10)The S-matrix no-go theorem [42] is not discussed here because it relies on slightly stronger assum”
TASI Lectures on Scattering Amplitudes (2017, result): “accordance with our stated philosophy these results will be derived without reference to an action. This concept of an “amplitudes bootstrap” closely follows the seminal work of Benincasa and Cachazo [25], though similar treatments can be found in the existing review literature [26, 27]. 3.1 Three-P”
Extensions of theories from soft limits (2016, methodology): “Another line of research which we only briefly started to explore is the use of extensions to “BCFW complete” a theory [40].”
Light-front higher-spin theories in flat space (2016, background): “In particular, there does exist a two-derivative gravitational vertex for a field of any spin [30–32], which is also evident in the language of amplitudes [33, 34].”
The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, background): “In fact, demanding consistency of the four-particle S-matrix leads to powerful constraints on the space of viable quantum field theories [2–4, 87].”