2007/04/30 by F. A. Dolan, F.A. Dolan · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.07.026
published as Nucl.Phys.B790:432-464,2008 · 38 pages, uses harvmac, v.2. references added, typos corrected, discussion of asymptotic counting included for more general chiral ring, v.3. typos corrected, discussion for su(2) simplified, to be published in Nuclear Physics B
openalex publication_date 2007/08/08 · arxiv created 2007/11/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free \N=4 super Yang Mills discussed, including a general result for large N. The partition function for BPS operators in the chiral ring of \N=4 super Yang Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free \N=4 super Yang Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.