### Abstract

We examine the extent to which pertubation theory, about the naive Goldstone vacuum in two dimensions, is able to reveal the true state of affairs - that there are no Goldstone modes and that the symmetry is restored for arbitrarily small coupling constant. We exploit the recent observation, by Elitzur, of the infrared finiteness of globally invariant Green functions to compute them to third non-trivial order in a variety of models. Applying the renormalization group to improve these calculations we argue that one can see cluster decomposition beginning to restore the symmetry. The perturbation theory's ignorance of the global topology means that we cannot follow the decay of the Green function out to infinity because of a "non-perturbative barrier". We comment on the relevance of this to "perturbative confinement" in QCD. We also examine the way in which the global topology influences the phase diagrams when we add the two-dimensional analogue of Higgs fields.

Original language | English (US) |
---|---|

Pages (from-to) | 169-188 |

Number of pages | 20 |

Journal | Nuclear Physics, Section B |

Volume | 163 |

Issue number | C |

DOIs | |

State | Published - 1980 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*163*(C), 169-188. https://doi.org/10.1016/0550-3213(80)90396-X

**Non-linear σ models : A perturbative approach to symmetry restoration.** / McKane, Alan; Stone, Michael.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 163, no. C, pp. 169-188. https://doi.org/10.1016/0550-3213(80)90396-X

}

TY - JOUR

T1 - Non-linear σ models

T2 - A perturbative approach to symmetry restoration

AU - McKane, Alan

AU - Stone, Michael

PY - 1980

Y1 - 1980

N2 - We examine the extent to which pertubation theory, about the naive Goldstone vacuum in two dimensions, is able to reveal the true state of affairs - that there are no Goldstone modes and that the symmetry is restored for arbitrarily small coupling constant. We exploit the recent observation, by Elitzur, of the infrared finiteness of globally invariant Green functions to compute them to third non-trivial order in a variety of models. Applying the renormalization group to improve these calculations we argue that one can see cluster decomposition beginning to restore the symmetry. The perturbation theory's ignorance of the global topology means that we cannot follow the decay of the Green function out to infinity because of a "non-perturbative barrier". We comment on the relevance of this to "perturbative confinement" in QCD. We also examine the way in which the global topology influences the phase diagrams when we add the two-dimensional analogue of Higgs fields.

AB - We examine the extent to which pertubation theory, about the naive Goldstone vacuum in two dimensions, is able to reveal the true state of affairs - that there are no Goldstone modes and that the symmetry is restored for arbitrarily small coupling constant. We exploit the recent observation, by Elitzur, of the infrared finiteness of globally invariant Green functions to compute them to third non-trivial order in a variety of models. Applying the renormalization group to improve these calculations we argue that one can see cluster decomposition beginning to restore the symmetry. The perturbation theory's ignorance of the global topology means that we cannot follow the decay of the Green function out to infinity because of a "non-perturbative barrier". We comment on the relevance of this to "perturbative confinement" in QCD. We also examine the way in which the global topology influences the phase diagrams when we add the two-dimensional analogue of Higgs fields.

UR - http://www.scopus.com/inward/record.url?scp=0642328083&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0642328083&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(80)90396-X

DO - 10.1016/0550-3213(80)90396-X

M3 - Article

AN - SCOPUS:0642328083

VL - 163

SP - 169

EP - 188

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - C

ER -