Establish the existence of a continuum limit along the line of constant physics

Establish whether increasing the lattice coupling β along the line of constant physics defined by the monopole-extended three-dimensional compact U(1) lattice gauge theory leads to a continuum limit.

Background

The paper modifies the three-dimensional compact U(1) lattice gauge theory by adding a monopole-number coupling μ to the Wilson action. By tuning β and μ simultaneously, the authors construct a trajectory on which the ratio of the lightest glueball mass to the square root of the string tension remains approximately constant, and they find that other low-lying mass ratios are likewise consistent with constant behavior.

The existence of this line of constant physics does not by itself establish a continuum quantum field theory. Along the trajectory, the string tension in lattice units decreases as β increases, which is consistent with—but does not prove—the presence of a critical point at finite β or at β = ∞. The available numerical data are insufficient to distinguish these possibilities from the alternative that no critical point exists and hence no continuum limit can be defined.