# Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach

## Abstract

We study the chiral phase transition for vectorlike SU(N) gauge theories as a function of the number of quark flavors N{sub f} by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for N{sub f}{lt}N, and apply it to larger values of N{sub f} where the phase transition is expected to occur. The new effective potential depends explicitly on the full {beta} function and the anomalous dimension {gamma} of the quark mass operator. By using this potential we argue that chiral symmetry is restored for {gamma}{lt}1. A perturbative computation of {gamma} then leads to an estimate of the critical value N{sub f}{sup c} for the transition. {copyright} {ital 1999} {ital The American Physical Society}

- Authors:

- Department of Physics, Yale University, New Haven, Connecticut 06520-8120 (United States)
- Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)

- Publication Date:

- OSTI Identifier:
- 362735

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D

- Additional Journal Information:
- Journal Volume: 60; Journal Issue: 5; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; CHIRAL SYMMETRY; PHASE TRANSFORMATIONS; SU GROUPS; GAUGE INVARIANCE; PERTURBATION THEORY; LAGRANGIAN FIELD THEORY

### Citation Formats

```
Sannino, F., and Schechter, J.
```*Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevD.60.056004.

```
Sannino, F., & Schechter, J.
```*Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach*. United States. doi:10.1103/PhysRevD.60.056004.

```
Sannino, F., and Schechter, J. Wed .
"Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach". United States. doi:10.1103/PhysRevD.60.056004.
```

```
@article{osti_362735,
```

title = {Chiral phase transition for SU(N) gauge theories via an effective Lagrangian approach},

author = {Sannino, F. and Schechter, J.},

abstractNote = {We study the chiral phase transition for vectorlike SU(N) gauge theories as a function of the number of quark flavors N{sub f} by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for N{sub f}{lt}N, and apply it to larger values of N{sub f} where the phase transition is expected to occur. The new effective potential depends explicitly on the full {beta} function and the anomalous dimension {gamma} of the quark mass operator. By using this potential we argue that chiral symmetry is restored for {gamma}{lt}1. A perturbative computation of {gamma} then leads to an estimate of the critical value N{sub f}{sup c} for the transition. {copyright} {ital 1999} {ital The American Physical Society}},

doi = {10.1103/PhysRevD.60.056004},

journal = {Physical Review, D},

number = 5,

volume = 60,

place = {United States},

year = {1999},

month = {9}

}