Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories

TL;DR

This paper develops a systematic method to construct and analyze gauge invariant operators in flavoured quiver gauge theories, extending previous frameworks to include flavour symmetries and providing explicit formulas for correlation functions.

Contribution

It introduces a diagonal basis for 2-point functions and generalizes Quiver Restricted Schur operators to flavoured cases, enabling detailed correlation function calculations.

Findings

Diagonal basis for gauge invariant operators established

Explicit 3-point function formulas derived

Networks of symmetric group coefficients used for computations

Abstract

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.