Glueballs and the Pomeron -- a Lattice Study

We perform lattice calculations of the lightest J=0,2,4,6 glueball masses in the D=3+1 SU(3) gauge theory and extrapolate to the continuum limit. Assuming that these masses lie on linear Regge trajectories we find a leading glueball trajectory alpha(t) = 0.93(24) + 0.28(2)alpha_R' t, where alpha_R' \simeq 0.9 {GeV}^{-2} is the slope of the usual mesonic Regge trajectories. This glueball trajectory has an intercept and slope similar to that of the Pomeron. We contrast this with the situation in D=2+1 where the leading glueball Regge trajectory is found to have too small an intercept to be important for high-energy cross-sections. We attempt to interpret the observed states and trajectories in terms of open and closed string models of glueballs.