Searching for a continuum 4D field theory arising from a 5D non-abelian gauge theory

The anisotropic 5D SU(2) Yang-Mills model has been widely investigated on the lattice during the last decade. In the case where all dimensions are large in size, it was previously claimed that there is a new phase in the phase diagram, called the Layer phase. In this phase, the gauge fields would be localized on 4D layers. Previous works claim that the phase transition to the Layer phase is of second order, which would allow a continuum limit to be taken. We present the extension of the previous work to large lattices, for which we found a first order phase transition. This leaves the scenario that this 5D theory can be dimensionally reduced to a continuum 4D field theory, doubtful.