Confinement at Weak Coupling

The free energy of U(N) and SU(N) gauge theory was recently found to be of order N^0 to all orders of a perturbative expansion about a center-symmetric orbit of vanishing curvature. Here I consider extended models for which this expansion is perturbatively stable. The extreme case of an SU(2) gauge theory whose configuration space is restricted to center-symmetric orbits has recently been investigated on the lattice hep-lat/0509156. In extension of my talk, a discussion and possible interpretation of the observed finite temperature phase transition is given. The transfer matrix of constrained SU(N) lattice gauge theory is constructed for any finite temperature.Comment: 8 pages, no figures, updated talk given at LC2005 in Cairns, Australi

Scale Anomaly Induced Instanton Interaction

The binary interaction of large size instantons in a SU(2) Yang-Mills theory is obtained from the one-loop effective action for the field strength. The instanton interaction is calculated as a function of the instanton separation and in dependence on radius and relative orientation of the instantons. Two equally oriented instantons with radii large compared with the scale defined by the gluon condensate have purely attractive interaction, whereas the interaction of maximal disoriented instantons is repulsive. We argue that the medium range attractive interaction of the instantons generally holds and is solely due to the instability of the perturbative vacuum.Comment: 11 LaTex pages (3 figures available on request), in press by Physics Letters B, UNITUE-THEP-4-199

Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge

Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.

The `BRST-invariant' Condensate of Dimension Two in QCD

The status of the `BRST-invariant' condensate of mass dimension two in QCD is explained. The condensate is only invariant under an `on-shell' BRST symmetry which includes a partial gauge-fixing. The on-shell BRST symmetry represents the residual gauge symmetry under gauge transformations which preserve the partial gauge fixing. The gauge-invariant operators which correspond to the BRST-invariant condensate are identified in the Lorentz and maximal Abelian gauges and are shown to be invariant under the residual gauge transformations.Comment: 6 page

Nonperturbative ghost dynamics in the maximal Abelian gauge

We construct the effective potential for the ghost condensate in the maximal Abelian gauge. This condensate is an order parameter for a global continuous symmetry, which is spontaneously broken since a nonvanishing value of lowers the vacuum energy. The associated Goldstone mode turns out to be unphysical.Comment: 16 pages. v2: version accepted for publication in JHE

Numerical study of gluon propagators in Maximally Abelian gauge

Propagators of diagonal and off-diagonal gluons are studied numerically in the Maximally Abelian gauge of the SU(2) lattice gauge theory. We have found the strong enhancement of the diagonal gluon in the infrared region. The enhancement factor is about 50 at the smallest available momentum, 325 MeV. We discuss also various analytical fits to the propagators.Comment: 3 pages, 3 figures, uses espcrc2.sty; Lattice2003(topology

Three loop MSbar renormalization of QCD in the maximal abelian gauge

We determine the three loop anomalous dimensions of the quark, centre and off-diagonal gluons, centre and off-diagonal ghosts and the gauge fixing parameters in the maximal abelian gauge for an arbitrary colour group in the MSbar renormalization scheme at three loops. We show that the three loop MSbar beta-function emerges from the renormalization of the centre gluon and also deduce the anomalous dimension of the BRST invariant dimension two mass operator. Moreover, we demonstrate that in the limit that the dimension of the centre of the group tends to zero, the anomalous dimensions of the quarks, off-diagonal gluons and off-diagonal ghosts tend to those of the quarks, gluons and ghosts of the Curci-Ferrari gauge respectively.Comment: 25 latex page

Semiclassical Casimir Energies at Finite Temperature

We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late

Monopole Condensation and Antisymmetric Tensor Fields: Compact QED and the Wilsonian RG Flow in Yang-Mills Theories

A field theoretic description of monopole condensation in strongly coupled gauge theories is given by actions involving antisymmetric tensors B_{\mu\nu} of rank 2. We rederive the corresponding action for 4d compact QED, summing explicitly over all possible monopole configurations. Its gauge symmetries and Ward identities are discussed. Then we consider the Wilsonian RGs for Yang-Mills theories in the presence of collective fields (again tensors B_{\mu\nu}) for the field strengths F_{\mu \nu} associated to the U(1) subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian action involving B_{\mu\nu}, whose validity corresponds to monopole condensation, constitutes a fixed point of the Wilsonian RG flow.Comment: 18 pages (LaTeX2e), 1 fi

On ghost condensation, mass generation and Abelian dominance in the Maximal Abelian Gauge

Recent work claimed that the off-diagonal gluons (and ghosts) in pure Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a dynamical mass through an off-diagonal ghost condensate. This condensation takes place due to a quartic ghost interaction, unavoidably present in MAG for renormalizability purposes. The off-diagonal mass can be seen as evidence for Abelian dominance. We discuss why ghost condensation of the type discussed in those works cannot be the reason for the off-diagonal mass and Abelian dominance, since it results in a tachyonic mass. We also point out what the full mechanism behind the generation of a real mass might look like.Comment: 7 pages; uses revtex