Mesonic chiral rings in Calabi–Yau cones from field theory

Abstract

We study the half-BPS mesonic chiral ring of the superconformal quiver theories arising from N D3-branes stacked at Ypq and Labc 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 Laba, 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.