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 $\sim 0.60$and$\sim 1.12$intheunitsofstringtension,or$\sim 0.28$and$\sim 0.52$ 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 a 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.