Phases ofZN lattice gauge theory

  • D. Boyanovsky


We use the Lagrangian formulation of theZN gauge theory in four dimensions and demonstrate its equivalence with the partition function for a Coulomb gas of electric and magnetic loops. This model is shown to be self-dual when expressed in the Villai form. It is found, as a lower bound, that forN<4 there are only two phases related by duality, while forN>4 three phases appear. The explicit calculation of the Wilson loop identifies them as electric confining, nonconfining and magnetic confining.

Фаэы 2Я рещеточной калибровочной теории


Мы испольэуем Лагранжианную формулировку 2Я калобровочной теории в четырех иэмерениях. Мы покаэываем зквивалентность зтого подхода функции раэделения для кулоновского гаэа злектрических и магнитных петель. Покаэывается, что зта модель является самодуальной, когда эаписывается в форме Виллиана. Обнаружено, что на нижней границе, для N<Л, имеется только две фаэы, свяэанные дуальностью, тогда как для N>4 появляются три фаэы. Явное вычисление петли Вильсона идентифицирует их, как злектрическое удержание, неудержание и магнитное удержание.


Si usa la formulazione lagrangiana della teoria di gaugeZN in quattro dimensioni e si dimostra la sua equivalenza con la funzione di partizione per un gas di Coulomb di cappi elettrici e magnetici. Si mostra che questo modello è autoduale quando lo si esprime nella forma di Villain. Si trova, come limite inferiore, che perN<4 ci sono solo due fasi che sono in relazione attraverso la dualità mentre perN>4 compaiono tre fasi. Il calcolo esplicito del cappio di Wilson li identifica come fase a confinamento elettrico, a non confinamento e a confinamento magnetico.


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Copyright information

© Società Italiana di Fisica 1979

Authors and Affiliations

  • D. Boyanovsky
    • 1
  1. 1.Centro Atómico BarilocheInstituto BalseiroArgentina

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