# Soft-collinear supersymmetry

## Abstract

Soft-Collinear E ective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the e ective Lagrangian for N = 1 SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the e ective Lagrangian for chiral SUSY theories with Yukawa couplings, speci cally the single avor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian | to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding elds along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. De ning the theory with respect to a speci c frame obfuscates Lorentz invariance | given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang- Mills in \collinear superspace",more »

- Authors:

- Univ. of Oregon, Eugene, OR (United States)
- Univ. of Oregon, Eugene, OR (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Reed College, Portland, OR (United States); Harvard Univ., Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of Oregon, Eugene, OR (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1367172

- Grant/Contract Number:
- SC0012567

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 3; 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; Superspaces; Supersymmetric Effective Theories; Supersymmetric gauge theory

### Citation Formats

```
Cohen, Timothy, Elor, Gilly, and Larkoski, Andrew J.
```*Soft-collinear supersymmetry*. United States: N. p., 2017.
Web. doi:10.1007/JHEP03(2017)017.

```
Cohen, Timothy, Elor, Gilly, & Larkoski, Andrew J.
```*Soft-collinear supersymmetry*. United States. doi:10.1007/JHEP03(2017)017.

```
Cohen, Timothy, Elor, Gilly, and Larkoski, Andrew J. Fri .
"Soft-collinear supersymmetry". United States.
doi:10.1007/JHEP03(2017)017. https://www.osti.gov/servlets/purl/1367172.
```

```
@article{osti_1367172,
```

title = {Soft-collinear supersymmetry},

author = {Cohen, Timothy and Elor, Gilly and Larkoski, Andrew J.},

abstractNote = {Soft-Collinear E ective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the e ective Lagrangian for N = 1 SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the e ective Lagrangian for chiral SUSY theories with Yukawa couplings, speci cally the single avor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian | to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding elds along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. De ning the theory with respect to a speci c frame obfuscates Lorentz invariance | given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang- Mills in \collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of super elds. As a byproduct, bootstrapping up to the full theory yields the rst algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. As a result, this work paves the way toward discovering the e ective theory for the collinear limit of N = 4 SUSY Yang-Mills.},

doi = {10.1007/JHEP03(2017)017},

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

number = 3,

volume = 2017,

place = {United States},

year = {Fri Mar 03 00:00:00 EST 2017},

month = {Fri Mar 03 00:00:00 EST 2017}

}