Half BPS states in AdS_5 x Y^{p,q}

TL;DR

This paper analyzes a class of half-BPS solutions in IIB supergravity asymptotic to AdS_5 x Y^{p,q}, connecting them to dual N=1 superconformal operators and computing their charges and conformal dimensions.

Contribution

It derives and analyzes differential equations describing 1/2 BPS geometries in AdS_5 x Y^{p,q} and relates these solutions to dual field theory operators, extending previous work on 1/8 BPS states.

Findings

Derived differential equations for 1/2 BPS geometries.

Computed global charges including R-charge.

Verified the conformal dimension relation D=3 R / 2.

Abstract

We study a class of solutions of IIB Supergravity which are asymptotically AdS_5 x Y^{p,q}. They have an R x SO(4) x SU(2) x U(1) isometry and preserve half of the 8 supercharges of the background geometry. They are described by a set of second order differential equations that we have found and analysed in a previous paper, where we studied 1/8 BPS states in the maximally supersymmetric AdS_5 x S^5 background. These geometries correspond to certain chiral primary operators of the N=1 superconformal quiver theories, dual to IIB theory on AdS_5 x Y^{p,q}. We also show how to recover the AdS_5 x Y^{p,q} backgrounds by suitably doubling the number of preserved supersymmetries. We then solve the differential equations perturbatively in a large AdS_5 radius expansion, imposing asymptotic AdS_5 x Y^{p,q} boundary conditions. We compute the global baryonic and mesonic charges, including the R-charge. As for the computation of the mass, i.e. the conformal dimension D of the dual field theory operators, which is notoriously subtle in asymptotically AdS backgrounds, we adopt the general formalism due to Wald and collaborators, which gives a finite result, and verify the relation D=3 R / 2, demanded by the N=1 superconformal algebra.