All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories
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 $$\lfloor$$ (n - 2)2 / 4 $$\rfloor$$ -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.
- Authors:
- Publication Date:
- Research Org.:
- Brown Univ., Providence, RI (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1465618
- Alternate Identifier(s):
- OSTI ID: 1498977
- Grant/Contract Number:
- SC0010010
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 121 Journal Issue: 8; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Prlina, Igor, Spradlin, Marcus, and Stanojevic, Stefan. All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories. United States: N. p., 2018.
Web. doi:10.1103/PhysRevLett.121.081601.
Prlina, Igor, Spradlin, Marcus, & Stanojevic, Stefan. All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories. United States. https://doi.org/10.1103/PhysRevLett.121.081601
Prlina, Igor, Spradlin, Marcus, and Stanojevic, Stefan. Tue .
"All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories". United States. https://doi.org/10.1103/PhysRevLett.121.081601.
@article{osti_1465618,
title = {All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories},
author = {Prlina, Igor and Spradlin, Marcus and Stanojevic, Stefan},
abstractNote = {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 $\lfloor$ (n - 2)2 / 4 $\rfloor$ -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.},
doi = {10.1103/PhysRevLett.121.081601},
journal = {Physical Review Letters},
number = 8,
volume = 121,
place = {United States},
year = {Tue Aug 21 00:00:00 EDT 2018},
month = {Tue Aug 21 00:00:00 EDT 2018}
}
https://doi.org/10.1103/PhysRevLett.121.081601
Web of Science
Figures / Tables:
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Figures / Tables found in this record: