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) similar or equal to 0.9 GeV-2 is the slope of the usual mesonic Regge trajectory. This glueball trajectory has an intercept and slope similar to that of the pomeron trajectory. 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 interpret the observed states and trajectories in terms of open and closed string models of glueballs. We discuss the large-N limit and perform an SU(8) calculation that hints at new states based on closed strings in higher representations. (C) 2004 Elsevier B.V. All rights reserved.
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