# Large-N reduction in QCD-like theories with massive adjoint fermions

## Abstract

Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 992967

- Report Number(s):
- SLAC-PUB-14152

arXiv:1006.0717; TRN: US1007876

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Journal Name:
- Phys.Rev.D82:125013,2010

- Additional Journal Information:
- Journal Name: Phys.Rev.D82:125013,2010

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FERMIONS; QUANTUM CHROMODYNAMICS; COMPUTERIZED SIMULATION; SYMMETRY; THERMODYNAMICS; YANG-MILLS THEORY; Lattice, Theory-HEP,HEPTH

### Citation Formats

```
Azeyanagi, Tatsuo, /Kyoto U., Hanada, Masanori, /Weizmann Inst., Unsal, Mithat, /Weizmann Inst. /SLAC /Stanford U., Phys. Dept., Yacoby, Ran, and /Weizmann Inst.
```*Large-N reduction in QCD-like theories with massive adjoint fermions*. United States: N. p., 2010.
Web. doi:10.1103/PhysRevD.82.125013.

```
Azeyanagi, Tatsuo, /Kyoto U., Hanada, Masanori, /Weizmann Inst., Unsal, Mithat, /Weizmann Inst. /SLAC /Stanford U., Phys. Dept., Yacoby, Ran, & /Weizmann Inst.
```*Large-N reduction in QCD-like theories with massive adjoint fermions*. United States. https://doi.org/10.1103/PhysRevD.82.125013

```
Azeyanagi, Tatsuo, /Kyoto U., Hanada, Masanori, /Weizmann Inst., Unsal, Mithat, /Weizmann Inst. /SLAC /Stanford U., Phys. Dept., Yacoby, Ran, and /Weizmann Inst. Thu .
"Large-N reduction in QCD-like theories with massive adjoint fermions". United States. https://doi.org/10.1103/PhysRevD.82.125013. https://www.osti.gov/servlets/purl/992967.
```

```
@article{osti_992967,
```

title = {Large-N reduction in QCD-like theories with massive adjoint fermions},

author = {Azeyanagi, Tatsuo and /Kyoto U. and Hanada, Masanori and /Weizmann Inst. and Unsal, Mithat and /Weizmann Inst. /SLAC /Stanford U., Phys. Dept. and Yacoby, Ran and /Weizmann Inst.},

abstractNote = {Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.},

doi = {10.1103/PhysRevD.82.125013},

url = {https://www.osti.gov/biblio/992967},
journal = {Phys.Rev.D82:125013,2010},

number = ,

volume = ,

place = {United States},

year = {2010},

month = {8}

}