Abstract
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group SO(N f ) in U(N c ) gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at N f = 6, belong to the scalar sector of \( \mathcal{N}=4 \) SYM. A simple formula is given for the two-point functions in the free field limit of g 2 Y M = 0. 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 N c , N f . 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.
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Kimura, Y., Ramgoolam, S. & Suzuki, R. Flavour singlets in gauge theory as permutations. J. High Energ. Phys. 2016, 142 (2016). https://doi.org/10.1007/JHEP12(2016)142
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DOI: https://doi.org/10.1007/JHEP12(2016)142