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Title: Lattice gluodynamics at negative g{sup 2}

Abstract

We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of {beta}=2N/g{sup 2} and for N=2 or 3. We show that in the limit {beta}{yields}-{infinity}, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected nonintersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g{sup 2} changes its sign which prevents us from having a convergent series in g{sup 2} for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of {beta}. For N=3, we derive an identity relating the observables at {beta} with those at {beta} rotated by {+-}2{pi}/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near {beta}=-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.

Authors:
;  [1]
  1. Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)
Publication Date:
OSTI Identifier:
20705764
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 71; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.71.016008; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GAUGE INVARIANCE; ISING MODEL; LATTICE FIELD THEORY; MULTIPLICITY; PATH INTEGRALS; PHASE TRANSFORMATIONS; SU GROUPS

Citation Formats

Li, L, and Meurice, Y. Lattice gluodynamics at negative g{sup 2}. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.71.016008.
Li, L, & Meurice, Y. Lattice gluodynamics at negative g{sup 2}. United States. https://doi.org/10.1103/PhysRevD.71.016008
Li, L, and Meurice, Y. 2005. "Lattice gluodynamics at negative g{sup 2}". United States. https://doi.org/10.1103/PhysRevD.71.016008.
@article{osti_20705764,
title = {Lattice gluodynamics at negative g{sup 2}},
author = {Li, L and Meurice, Y},
abstractNote = {We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of {beta}=2N/g{sup 2} and for N=2 or 3. We show that in the limit {beta}{yields}-{infinity}, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected nonintersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g{sup 2} changes its sign which prevents us from having a convergent series in g{sup 2} for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of {beta}. For N=3, we derive an identity relating the observables at {beta} with those at {beta} rotated by {+-}2{pi}/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near {beta}=-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.},
doi = {10.1103/PhysRevD.71.016008},
url = {https://www.osti.gov/biblio/20705764}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 1,
volume = 71,
place = {United States},
year = {Sat Jan 01 00:00:00 EST 2005},
month = {Sat Jan 01 00:00:00 EST 2005}
}