# Supersymmetric color superconductivity

## Abstract

Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N{sub c}) gauge theories with N{sub f} flavors of quarks in the presence of a baryon chemical potential {mu}, and describe the global symmetry breaking patterns at low energy. Our analysis requires {mu} < {Lambda} and is thus complementary to the variational approach that has been successful for {mu} >> {Lambda}. We find that for N{sub F} < N{sub c} a modified U(1){sub B} symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N{sub f} = N{sub c} there is a critical chemical potential above which the U(1){sub B} is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N{sub c} + 1 {le} N{sub f} < 3/2 N{sub c} and find that baryon number is broken dynamically for {mu} > {mu}{sub c}. We also give a qualitative description of the phasesmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director. Office of Science. Office of High Energy and Nuclear Physics. Division of High Energy Physics; National Science Foundation Grant PHY-0098840; Institute for Advanced Study

- OSTI Identifier:
- 842549

- Report Number(s):
- LBNL-53793

R&D Project: PTHOPS; TRN: US0503613

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Journal Article

- Resource Relation:
- Other Information: Journal Publication Date: 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BARYON NUMBER; BARYONS; COLOR; QUANTUM CHROMODYNAMICS; QUARKS; SPURIONS; SUPERCONDUCTIVITY; SYMMETRY; SYMMETRY BREAKING; VECTORS

### Citation Formats

```
Harnik, Roni, Larson, Daniel T., and Murayama, Hitoshi.
```*Supersymmetric color superconductivity*. United States: N. p., 2003.
Web.

```
Harnik, Roni, Larson, Daniel T., & Murayama, Hitoshi.
```*Supersymmetric color superconductivity*. United States.

```
Harnik, Roni, Larson, Daniel T., and Murayama, Hitoshi. Thu .
"Supersymmetric color superconductivity". United States.
doi:. https://www.osti.gov/servlets/purl/842549.
```

```
@article{osti_842549,
```

title = {Supersymmetric color superconductivity},

author = {Harnik, Roni and Larson, Daniel T. and Murayama, Hitoshi},

abstractNote = {Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N{sub c}) gauge theories with N{sub f} flavors of quarks in the presence of a baryon chemical potential {mu}, and describe the global symmetry breaking patterns at low energy. Our analysis requires {mu} < {Lambda} and is thus complementary to the variational approach that has been successful for {mu} >> {Lambda}. We find that for N{sub F} < N{sub c} a modified U(1){sub B} symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N{sub f} = N{sub c} there is a critical chemical potential above which the U(1){sub B} is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N{sub c} + 1 {le} N{sub f} < 3/2 N{sub c} and find that baryon number is broken dynamically for {mu} > {mu}{sub c}. We also give a qualitative description of the phases in the ''conformal window'', 3/2 N{sub c} < N{sub f} < 3N{sub c}, at finite density.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Sep 18 00:00:00 EDT 2003},

month = {Thu Sep 18 00:00:00 EDT 2003}

}