We extend to large lattices the work of a previous investigation of the phase diagram of the anisotropic five-dimensional SU(2) Yang-Mills model using Monte Carlo simulations in the regime where the lattice spacing in the fifth dimension is larger than in the other four dimensions. We find a first order phase transition between the confining and deconfining phase at the anisotropic parameter point β 4 = 2.60 which was previously claimed to be the critical point at which the order of the transition changes from first to second. We conclude that large lattices are required to establish the first order nature of this line of transitions and consequently that the scenario of dimensional reduction of the five-dimensional theory to a continuum four-dimensional theory via the existence of the so-called "layer phase" is unpromising.

The phase diagram of five-dimensional anisotropic gauge theories in a flat background has been extensively explored during the last decade. Here, we present novel results for the phase structure of the five-dimensional anisotropic SU(2) model embedded in a warped background. The static potential in the deconfining region of the phase diagram, close to the transition to the layered phase, provides evidence of a Yukawa mass, suggesting that the system is in a 4D Higgs-like phase. As no symmetry has been broken by the boundary conditions, this phase appears to be due to the warp factor. Whether the system is dimensionally reduced from a 5D phase to this 4D Higgs-like phase, which would provide a mechanism for dimensional reduction via localization, remains open.Edinburgh 2015/23

We present preliminary results to determine the strong coupling constant by using the gradient flow. Pure SU(3) gauge theory is studied. We carry out a direct analysis on very fine zero temperature lattices where the gradient flow is calculated in the continuum limit. As a second method we applied the finite-size scaling method to move towards the perturbative regime.

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The phase diagram of five-dimensional anisotropic gauge theories in a flat background has been extensively explored during the last decade. Here, we present novel results for the phase structure of the five-dimensional anisotropic SU(2) model embedded in a warped background. The static potential in the deconfining region of the phase diagram, close to the transition to the layered phase, provides evidence of a Yukawa mass, suggesting that the system is in a 4D Higgs-like phase. As no symmetry has been broken by the boundary conditions, this phase appears to be due to the warp factor. Whether the system is dimensionally reduced from a 5D phase to this 4D Higgs-like phase, which would provide a mechanism for dimensional reduction via localization, remains open.