Abstract
We extend on-shell bootstrap methods from spacetime amplitudes to the worldsheet objects of the CHY formalism. We find that the integrands corresponding to tree-level non-linear sigma model, Yang-Mills and $(DF)^2$ theory are determined by demanding enhanced UV scaling under BCFW shifts. Back in spacetime, we also find that $(DF)^2$ theory is fixed by gauge invariance/UV scaling and simple locality assumptions.
Highlights
The S-matrix bootstrap program aims to construct scattering amplitudes directly from on-shell physical principles, foregoing the complicated formalisms of off-shell Lagrangians or Feynman diagrams
We find that a step in this direction is given by the Cachazo-He-Yuan formalism [32,33,34,35,36,37,38,39], which can be viewed as a transform from spacetime to a world sheet, where local singularities corresponding to propagators are replaced by world sheet singularities ðσi − σjÞ−1, with the precise map encoded in the scattering equations (SEs) (6)
We propose that simple scaling under BCFW shifts is sufficient to fully determine the integrands relevant for nonlinear sigma model (NLSM), YM, as well as DF2 theory [42], even without assuming the scattering equations
Summary
The S-matrix bootstrap program aims to construct scattering amplitudes directly from on-shell physical principles, foregoing the complicated formalisms of off-shell Lagrangians or Feynman diagrams. It has been discovered that amplitudes can be fully determined with even less information than previously thought: gauge invariance or the Adler zero [11,12,13,14,15], Bern-Carrasco-Johansson (BCJ) relations [16], IR behavior [17], or UV scaling [16,18], together with simple locality assumptions, is each sufficient to fully constrain a wide range of tree level amplitudes, including their unitarity (factorization) III–V, we present evidence that the integrands relevant for NLSM, Yang-Mills (YM), and DF2 theory are fully determined by UV scaling and various assumptions Motivated by this result, we extend such observations to the usual spacetime DF2 amplitudes, which we find to be fixed by gauge invariance and similar UV conditions.
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