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Abstract: The free field partition function for a generic UN gauge theory, where thefundamental fields transform in the adjoint representation, is analysed interms of symmetric polynomial techniques. It is shown by these means how thisis related to the cycle polynomial for the symmetric group and how the large Nresult may be easily recovered. Higher order corrections for finite N are alsodiscussed in terms of symmetric group characters. For finite N, the partitionfunction involving a single bosonic fundamental field is recovered and explicitcounting of multi-trace quarter BPS operators in free \N=4 super Yang Millsdiscussed, including a general result for large N. The partition function forBPS operators in the chiral ring of \N=4 super Yang Mills is analysed in termsof plane partitions. Asymptotic counting of BPS primary operators withdiffering R-symmetry charges is discussed in both free \N=4 super Yang Millsand in the chiral ring. Also, general and explicit expressions are derived forSU2 gauge theory partition functions, when the fundamental fields transformin the adjoint, for free field theory.

Autor: F.A. Dolan


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