Simple Encoding of Higher-Derivative Gauge and Gravity Counterterms.

Invoking increasingly higher dimension operators to encode novel UV physics in effective gauge and gravity theories traditionally means working with increasingly more finicky and difficult expressions. We find that the duality between color and kinematics provides a powerful tool towards drastic simplification. Local higher-derivative gauge and gravity operators at four points can be absorbed into simpler higher-derivative corrections to scalar theories, requiring only a small number of building blocks to generate gauge and gravity four-point amplitudes to all orders in mass dimension.

Scattering Amplitudes from Soft Theorems and Infrared Behavior.

We prove that soft theorems uniquely fix tree-level scattering amplitudes in a wide range of massless theories, including Yang-Mills, gravity, the nonlinear sigma model, Dirac-Born-Infeld, dilaton effective theories, extended theories like the NLSM⊕ϕ^{3} (nonlinear sigma model ϕ^{3}), as well as some higher derivative corrections to these theories. We conjecture the same is true even when imposing more general soft behavior, simply by assuming the existence of soft operators, or by imposing gauge invariance or the Adler zero only up to a finite order in soft expansions. Besides reproducing known amplitudes, this analysis reveals a new higher order correction to the NLSM and two interesting facts: the subleading theorem for the dilaton, and the subsubleading theorem for DBI follow automatically from the more leading theorems. These results provide motivation that asymptotic symmetries contain enough information to fully fix a holographic S matrix.

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance.

We conjecture that the leading two-derivative tree-level amplitudes for gluons and gravitons can be derived from gauge invariance together with mild assumptions on their singularity structure. Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge invariance in just n-1 particles together with minimal power counting uniquely fixes the amplitude. Unitarity in the form of factorization then follows from locality and gauge invariance. We also give evidence for a stronger conjecture: assuming only that singularities occur when the sum of a subset of external momenta go on shell, we show in nontrivial examples that gauge invariance and power counting demand a graph structure for singularities. Thus, both locality and unitarity emerge from singularities and gauge invariance. Similar statements hold for theories of Goldstone bosons like the nonlinear sigma model and Dirac-Born-Infeld by replacing the condition of gauge invariance with an appropriate degree of vanishing in soft limits.