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Particles and Fields
Eur. Phys. J. C 28, 415-424 (2003)
DOI: 10.1140/epjc/s2003-01170-0

Confinement and mass gap in abelian gauge

U. Ellwanger1 and N. Wschebor1, 2

1  Laboratoire de Physique Théorique $^{\ast}$, Université de Paris XI, Bâtiment 210, 91405 Orsay Cedex, France
2  Instituto de Física, Facultad de Ingeniería (C.C. 30, CP 1100), Montevideo, Uruguay

(Received: 27 November 2002 / Published online: 14 April 2003 )

First, we present a simple confining abelian pure gauge theory. Classically, its kinetic term is not positive definite, and it contains a simple UV regularized F4 interaction. This provokes the formation of a condensate $\phi \sim F^2$ such that, at the saddle point $\widehat{\phi}$ of the effective potential, the wave function normalization constant of the abelian gauge fields $Z_{\mathrm {eff}}(\widehat{\phi})$ vanishes exactly. Then we study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an auxiliary field $\rho$ for a BRST invariant condensate of dimension 2, which renders the charged sector massive. Under simple assumptions its effective low energy theory reduces to the confining abelian model discussed before, and the VEV of $\rho$ is seen to scale correctly with the renormalization point. Under these assumptions, the confinement condition Zeff = 0 also holds for the massive charged sector, which suppresses the couplings of the charged fields to the abelian gauge bosons in the infrared regime.

© Società Italiana di Fisica, Springer-Verlag 2003