Flavour singlets in gauge theory as Permutations
arXiv:1608.03188 · doi:10.1007/JHEP12(2016)142
Abstract
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group in gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at , belong to the scalar sector of SYM. A simple formula is given for the two-point functions in the free field limit of . The free two-point functions are shown to be equal to the partition function on a 2-complex with boundaries and a defect, in a topological field theory of permutations. The permutation equivalence classes are Fourier transformed to a representation basis which is orthogonal for the two-point functions at finite . Counting formulae for the gauge-invariant operators are described. The one-loop mixing matrix is derived as a linear operator on the permutation equivalence classes.
50 pages, v2: typos corrected, v3: to appear in JHEP
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