# Unifying relations for scattering amplitudes

## Abstract

We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. With this being said, transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
- Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Thoretical Physics
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Univ. of California, Los Angeles, CA (United States). Mani L. Bhaumik Inst. for Thoretical Physics

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1501900

- Grant/Contract Number:
- SC0010255

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Scattering Amplitudes

### Citation Formats

```
Cheung, Clifford, Shen, Chia-Hsien, and Wen, Congkao.
```*Unifying relations for scattering amplitudes*. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)095.

```
Cheung, Clifford, Shen, Chia-Hsien, & Wen, Congkao.
```*Unifying relations for scattering amplitudes*. United States. doi:10.1007/jhep02(2018)095.

```
Cheung, Clifford, Shen, Chia-Hsien, and Wen, Congkao. Thu .
"Unifying relations for scattering amplitudes". United States. doi:10.1007/jhep02(2018)095. https://www.osti.gov/servlets/purl/1501900.
```

```
@article{osti_1501900,
```

title = {Unifying relations for scattering amplitudes},

author = {Cheung, Clifford and Shen, Chia-Hsien and Wen, Congkao},

abstractNote = {We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. With this being said, transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.},

doi = {10.1007/jhep02(2018)095},

journal = {Journal of High Energy Physics (Online)},

issn = {1029-8479},

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}