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.
Highlights
Finite N aspects of AdS/CFT [1,2,3], such as giant gravitons [4], the stringy exclusion principle [5] and LLM geometries [6], have motivated the study of multi-matrix sectors of N = 4 SYM, associated with different BPS sectors of the theory
We follow the usual convention according to which round nodes in the quiver correspond to gauge groups, whereas square nodes correspond to global symmetries
In this paper we considered free quiver gauge theories with gauge group n a=1
Summary
We will be concerned with the construction of a basis for the Hilbert space of holomorphic matrix invariants for the class of quiver gauge theories with a U (Na) gauge group and a SU (Fa)×SU (Fa)×U (1) flavour group The Quiver Restricted Schur polynomials are orthogonal in the free field metric, as we will show, even for flavoured gauge theories This leads to the simple expression for the two point function in eq (4.1): OQ(L) OQ† (L ) = δL,L cn fNa(Ra). This can be viewed as a dual basis where representation theory is used to perform a Fourier transformation on the equivalence classes of the permutation description We refer to these gauge invariants, polynomial in the bi-fundamental and fundamental matter fields, as Quiver Restricted Schur polynomials.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
