Study on the nonperturbative existence of Yang-Mills theories with large extra dimensions

Pure lattice SU(2) Yang-Mills theory in five dimensions is considered, where an extra dimension is compactified on a circle. Monte Carlo simulations indicate that the theory possesses a continuum limit with a nonvanishing string tension if the compactification radius is smaller than a certain value R-M which is O(1/10) of the inverse of the square root of the string tension. We verify nonperturbatively the power-law running of the gauge coupling constant. Our method can be applied to the investigation of continuum limits in other higher-dimensional gauge theories.