Flavour singlets in gauge theory as permutations

Author(s)

Kimura, Yusuke ; Ramgoolam, Sanjaye ; Suzuki, Ryo

• Document type: Journal article
• Source: Journal of High Energy Physics; v. N/A, n. 12, p. 46-pg., 2016-12-28.

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 N = 4 SYM. A simple formula is given for the two-point functions in the free field limit of g(YM)(2) = 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. (AU)

• FAPESP's process: 11/11973-4 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics
• Grantee: Nathan Jacob Berkovits
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/04030-7 - Integrability in Gauge theories
• Grantee: Ryo Suzuki
• Support Opportunities: Scholarships in Brazil - Post-Doctoral