# 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:

- Brown Univ., Providence, RI (United States). Dept. of Physics
- 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}

}

DOI: 10.1103/physrevlett.121.081601

*Citation information provided by*

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Web of Science

#### Figures / Tables:

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*