Glueballs and k-strings in SU(N) gauge theories:: calculations with improved operators -: art. no. 012

We test a variety of blocking and smearing algorithms for constructing glueball and string wave-functionals, and find some with much improved overlaps onto the lightest states. We use these algorithms to obtain improved results on the tensions of k-strings in SU(4), SU(6), and SU(8) gauge theories. We emphasise the major systematic errors that still need to be controlled in calculations of heavier k-strings, and perform calculations in SU(4) on an anisotropic lattice in a bid to minimise one of these. All these results point to the k-string tensions lying part-way between the 'MQCD' and 'Casimir Scaling' conjectures, with the power in 1/N of the leading correction lying is an element of [1, 2]. We also obtain some evidence for the presence of quasi-stable strings in calculations that do not use sources, and observe some near-degeneracies between (excited) strings in different representations. We also calculate the lightest glueball masses for N = 2,...,8, and extrapolate to N = infinity, obtaining results compatible with earlier work. We show that the N = infinity factorisation of the euclidean correlators that are used in such mass calculations does not make the masses any less calculable at large N.