# Spontaneous supersymmetry breaking in two dimensional lattice super QCD

## Abstract

We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N _{f} fermions in the fundamental representation of a U(N _{c}) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetry breaks spontaneously when N _{f} < N _{c} in agreement with theoretical expectations.

- Authors:

- Syracuse Univ., Syracuse, NY (United States)
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1226321

- Report Number(s):
- FERMILAB-PUB-15-497-T

Journal ID: ISSN 1029-8479; arXiv eprint number arXiv:1505.00467

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; supersymmetry breaking; spontaneous symmetry breaking; Beyond Standard Model; lattice gauge field theories

### Citation Formats

```
Catterall, Simon, and Veernala, Aarti. Spontaneous supersymmetry breaking in two dimensional lattice super QCD. United States: N. p., 2015.
Web. doi:10.1007/JHEP10(2015)013.
```

```
Catterall, Simon, & Veernala, Aarti. Spontaneous supersymmetry breaking in two dimensional lattice super QCD. United States. doi:10.1007/JHEP10(2015)013.
```

```
Catterall, Simon, and Veernala, Aarti. Fri .
"Spontaneous supersymmetry breaking in two dimensional lattice super QCD". United States. doi:10.1007/JHEP10(2015)013. https://www.osti.gov/servlets/purl/1226321.
```

```
@article{osti_1226321,
```

title = {Spontaneous supersymmetry breaking in two dimensional lattice super QCD},

author = {Catterall, Simon and Veernala, Aarti},

abstractNote = {We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains Nf fermions in the fundamental representation of a U(Nc) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetry breaks spontaneously when Nf < Nc in agreement with theoretical expectations.},

doi = {10.1007/JHEP10(2015)013},

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

number = 10,

volume = 2015,

place = {United States},

year = {2015},

month = {10}

}

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Works referenced in this record:

##
A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges

journal, September 2005

- Kaplan, David B.; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2005, Issue 09

##
Testing a novel large- *N* reduction for 𝒩 = 4 super Yang-Mills theory on *R* × *S* ^{3}

journal, September 2009

- Ishiki, Goro; Kim, Sang-Woo; Nishimura, Jun
- Journal of High Energy Physics, Vol. 2009, Issue 09

##
Phases of N = 2 theories in two dimensions

journal, August 1993

- Witten, Edward
- Nuclear Physics B, Vol. 403, Issue 1-2

##
Parallel software for lattice $\mathcal{N}=4$ supersymmetric Yang–Mills theory

journal, May 2015

- Schaich, David; DeGrand, Thomas
- Computer Physics Communications, Vol. 190

##
Classification of supersymmetric lattice gauge theories by orbifolding

journal, July 2007

- Damgaard, Poul H.; Matsuura, So
- Journal of High Energy Physics, Vol. 2007, Issue 07

##
Phase structure of lattice $\mathcal{N}=4$ super Yang-Mills

journal, November 2012

- Catterall, Simon; Damgaard, Poul H.; DeGrand, Thomas
- Journal of High Energy Physics, Vol. 2012, Issue 11

##
Holographic description of a quantum black hole on a computer

journal, April 2014

- Hanada, M.; Hyakutake, Y.; Ishiki, G.
- Science, Vol. 344, Issue 6186

##
Lattice formulation of Script N = 4 super Yang-Mills theory

journal, June 2005

- Catterall, Simon
- Journal of High Energy Physics, Vol. 2005, Issue 06

##
Simulations of Script N = 2 super Yang-Mills theory in two dimensions

journal, March 2006

- Catterall, Simon
- Journal of High Energy Physics, Vol. 2006, Issue 03

##
From twisted supersymmetry to orbifold lattices

journal, January 2008

- Catterall, Simon
- Journal of High Energy Physics, Vol. 2008, Issue 01

##
Supersymmetry on a euclidean spacetime lattice 2. Target theories with eight supercharges

journal, December 2003

- Cohen, Andrew G.; Kaplan, David B.; Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2003, Issue 12

##
Exact extended supersymmetry on a lattice: Twisted <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> super-Yang–Mills in two dimensions

journal, February 2006

- D'Adda, Alessandro; Kanamori, Issaku; Kawamoto, Noboru
- Physics Letters B, Vol. 633, Issue 4-5

##
Twisted supersymmetric gauge theories and orbifold lattices

journal, October 2006

- Ünsal, Mithat
- Journal of High Energy Physics, Vol. 2006, Issue 10

##
Exact lattice supersymmetry

journal, November 2009

- Catterall, Simon; Kaplan, David B.; Ünsal, Mithat
- Physics Reports, Vol. 484, Issue 3-4

##
A geometrical approach to *N* =2 super Yang-Mills theory on the two dimensional lattice

journal, November 2004

- Catterall, Simon
- Journal of High Energy Physics, Vol. 2004, Issue 11

##
Geometry of orbifolded supersymmetric lattice gauge theories

journal, March 2008

- Damgaard, Poul H.; Matsuura, So
- Physics Letters B, Vol. 661, Issue 1

##
Real space renormalization group for twisted lattice N $$ \mathcal{N} $$ =4 super Yang-Mills

journal, November 2014

- Catterall, Simon; Giedt, Joel
- Journal of High Energy Physics, Vol. 2014, Issue 11

##
Two-Dimensional Lattice for Four-Dimensional = 4 Supersymmetric Yang-Mills

journal, October 2011

- Hanada, M.; Matsuura, S.; Sugino, F.
- Progress of Theoretical Physics, Vol. 126, Issue 4

##
An object oriented code for simulating supersymmetric Yang–Mills theories

journal, June 2012

- Catterall, Simon; Joseph, Anosh
- Computer Physics Communications, Vol. 183, Issue 6

##
Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry

journal, March 2004

- Sugino, Fumihiko
- Journal of High Energy Physics, Vol. 2004, Issue 03

##
On the sign problem in 2D lattice super Yang-Mills

journal, January 2012

- Catterall, Simon; Galvez, Richard; Joseph, Anosh
- Journal of High Energy Physics, Vol. 2012, Issue 1

##
Aspects of non-abelian gauge dynamics in two-dimensional Script N = (2,2) theories

journal, May 2007

- Hori, Kentaro; Tong, David
- Journal of High Energy Physics, Vol. 2007, Issue 05

##
Lattice formulation of three-dimensional $ \mathcal{N}=4 $ gauge theory with fundamental matter fields

journal, September 2013

- Joseph, Anosh
- Journal of High Energy Physics, Vol. 2013, Issue 9

##
Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges

journal, August 2003

- Cohen, Andrew G.; Kaplan, David B.; Katz, Emanuel
- Journal of High Energy Physics, Vol. 2003, Issue 08

##
Perturbative renormalization of lattice $ \mathcal{N} = 4 $ super Yang-Mills theory

journal, April 2011

- Catterall, Simon; Dzienkowski, Eric; Giedt, Joel
- Journal of High Energy Physics, Vol. 2011, Issue 4

##
Two-dimensional 𝒩 = (2, 2) supersymmetric lattice gauge theory with matter fields in the fundamental representation

journal, July 2008

- Matsuura, So
- Journal of High Energy Physics, Vol. 2008, Issue 07

##
Twisted supersymmetries in lattice $ \mathcal{N} $ = 4 super Yang-Mills theory

journal, October 2013

- Catterall, Simon; Giedt, Joel; Joseph, Anosh
- Journal of High Energy Physics, Vol. 2013, Issue 10

##
Dynamical breaking of supersymmetry

journal, October 1981

- Witten, Edward
- Nuclear Physics B, Vol. 188, Issue 3