Gauge invariants and correlators in flavoured quiver gauge theories. (English) Zbl 1346.81078
Summary: In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 16G20 | Representations of quivers and partially ordered sets |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 20B30 | Symmetric groups |
| 20C35 | Applications of group representations to physics and other areas of science |
| 46T25 | Holomorphic maps in nonlinear functional analysis |
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