Induced QCD and Hidden Local ZN Symmetry

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for non-singlets average to zero. We argue that, if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support presence of such a phase transition

Quantum self-consistency of AdS×ΣAdS \times \Sigma brane models

Continuing on our previous work, we consider a class of higher dimensional brane models with the topology of $AdS_{D_1+1} \times \Sigma$, where $\Sigma$ is a one-parameter compact manifold and two branes of codimension 1 are located at the orbifold fixed points. We consider a set-up where such a solution arises from Einstein-Yang-Mills theory and evaluate the one-loop effective potential induced by gauge fields and by a generic bulk scalar field. We show that this type of brane models resolves the gauge hierarchy between the Planck and electroweak scales through redshift effects due to the warp factor $a=e^{-\pi kr}$. The value of $a$ is then fixed by minimizing the effective potential. We find that, as in the Randall Sundrum case, the gauge field contribution to the effective potential stabilises the hierarchy without fine-tuning as long as the laplacian $\Delta_\Sigma$ on $\Sigma$ has a zero eigenvalue. Scalar fields can stabilise the hierarchy depending on the mass and the non-minimal coupling. We also address the quantum self-consistency of the solution, showing that the classical brane solution is not spoiled by quantum effects.Comment: 10 page