All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories.

Igor Prlina,Stefan Stanojevic,Marcus Spradlin

doi:10.1103/physrevlett.121.081601

Igor Prlina, Stefan Stanojevic + Show 1 more

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https://doi.org/10.1103/physrevlett.121.081601

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Abstract

In massless quantum field theories the Landau equations are invariant under graph operations familiar from the theory of electrical circuits. Using a theorem on the Y-Δ reducibility of planar circuits we prove that the set of first-type Landau singularities of an n-particle scattering amplitude in any massless planar theory, at any finite loop order, is a subset of those of a certain n-particle ⌊(n-2)^{2}/4⌋-loop "ziggurat" graph. We determine this singularity locus explicitly for n=6 and find that it corresponds precisely to the vanishing of the symbol letters familiar from the hexagon bootstrap in supersymmetric Yang-Mills (SYM) theory. Further implications for SYM theory are discussed.

Highlights

Introduction.—For over half a century, much has been learned from the study of singularities of scattering amplitudes in quantum field theory, an important class of which are encoded in the Landau equations [1]
We conclude that the n-particle bðn − 2Þ2=4c-loop ziggurat graph encodes all possible first-type Landau singularities of any n-particle amplitude at any finite loop order in any massless planar theory
VI, we discuss several interesting implications of our result for planar N 1⁄4 4 supersymmetric Yang-Mills (SYM) theory, which provided the motivation for this work [7,8,9,10]

Summary

Introduction

Introduction.—For over half a century, much has been learned from the study of singularities of scattering amplitudes in quantum field theory, an important class of which are encoded in the Landau equations [1]. We conclude that the n-particle bðn − 2Þ2=4c-loop ziggurat graph encodes all possible first-type Landau singularities of any n-particle amplitude at any finite loop order in any massless planar theory. It is conventional to discuss scattering amplitudes for a fixed number n of external particles, each of which carries some momentum pi that in massless theories satisfies p2i 1⁄4 0.

Results

Conclusion