Revisiting glueball wave functions at zero and finite temperature

We study the sizes and thermal properties of glueballs in a three-dimensional compact Abelian gauge model on improved lattice. We predict the radii of ∼0.60 and ∼1.12 in the units of string tension, or ∼0.28 and ∼0.52 fm, for the scalar and tensor glueballs, respectively. We perform a well controlled extrapolation of the radii to the continuum limit and observe that our results agree with the predicted values. Using Monte Carlo simulations, we extract the pole mass of the lowest scalar and tensor glueballs from the temporal correlators at finite temperature. We see clear evidence of the deconfined phase, and the transition appears to be similar to that of the two-dimensional XY model as expected from universality arguments. Our results show no significant changes in the glueball wave functions and masses in the deconfined phase.