Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory

TL;DR

This paper analyzes the structure of mesonic chiral rings in N=1 superconformal quiver theories from D3-branes at Calabi-Yau singularities, connecting gauge theory operators with geometric invariants and bulk gravity states.

Contribution

It provides a detailed mapping between gauge invariant operators and geometric monomials, and constructs a finite N partition function matching gravity dual interpretations.

Findings

Partition function matches bulk gravity for smooth geometries.

Extra operators in singular geometries relate to localized twisted states.

Chiral ring states correspond to cohomologically trivial giant gravitons.

Abstract

We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry. This map enables us to write a partition function at finite N over mesonic half-BPS states. It agrees with the bulk gravity interpretation of chiral ring states as cohomologically trivial giant gravitons. The quiver theories for L^aba, which have singular base geometries, contain extra operators not counted by the naive bulk partition function. These extra operators have a natural interpretation in terms of twisted states localized at the orbifold-like singularities in the bulk.