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Title: 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:
 [1];  [2];  [1]
  1. Brown Univ., Providence, RI (United States). Dept. of Physics
  2. Brown Univ., Providence, RI (United States). Dept. of Physics; School of Natural Sciences, Princeton, NJ (United States). Inst. for Advanced Study
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 Volume: 121; Journal Issue: 8; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
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. doi:10.1103/physrevlett.121.081601.
Prlina, Igor, Spradlin, Marcus, and Stanojevic, Stefan. Wed . "All-Loop Singularities of Scattering Amplitudes in Massless Planar Theories". United States. doi: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 = {2018},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/physrevlett.121.081601

Citation Metrics:
Cited by: 1 work
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Figures / Tables:

Figure 1 Figure 1: Elementary circuit moves that preserve solution sets of the massless Landau equations: (a) series reduction, (b) parallel reduction, and (c) Y-Δ reduction.

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