Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory

Abstract

We investigate the scaling behaviour of gauge-ball masses and static potential in the pure U(1) lattice gauge theory on toroidal lattices. An extended gauge field action $-\sum_P(β\cosΘ_P + γ\cos2Θ_P)$ is used with $γ= -0.2$ and -0.5. Gauge-ball correlation functions with all possible lattice quantum numbers are calculated. Most gauge-ball masses scale with the non-Gaussian exponent $ν_{ng}\approx 0.36$. The $A_1^{++}$ gauge-ball mass scales with the Gaussian value $ν_{g} \approx 0.5$ in the investigated range of correlation lengths. The static potential is examined with Sommer's method. The long range part scales consistently with $ν_{ng}$ but the short range part tends to yield smaller values of $ν$. The $β$-function, having a UV stable zero, is obtained from the running coupling. These results hold for both $γ$ values, supporting universality. Consequences for the continuum limit of the theory are discussed.