From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr

TL;DR

This paper explores the AdS/CFT duality between Sasaki-Einstein spaces and quiver gauge theories using BPS geodesics, focusing on toric Lpqr geometries to establish precise correspondences and new relations.

Contribution

It determines dual quivers and BPS spectra for Lpqr geometries, linking geometric parameters to field theory via BPS geodesics and extending the duality understanding.

Findings

Matched mesonic operator quantum numbers with geodesic momenta.

Derived relations between geometric parameters and field theory via BPS spectra.

Identified special cases corresponding to known generalized conifolds.

Abstract

The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analysis simplifies for the special case of the Lpqq models, which are shown to correspond to the known "generalized conifolds". These geometries can break conformal invariance through toric deformations of the complex structure.