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

Sergio Benvenuti, Martin Kruczenski

TL;DR

This work analyzes massless BPS geodesics in the toric Sasaki–Einstein spaces L^{p,q|r} within the AdS/CFT framework, establishing a precise correspondence with BPS mesons in the dual quiver gauge theories. By deriving an R-charge angle from the holomorphic three-form and mapping the toric GLSM data to quiver blocks, the authors connect geometric parameters to a-maximization data, validating the duality through central charges and volumes. They show that extremal geodesics correspond to four corner mesons, and that the a-maximization results precisely reproduce the geometric volumes via a = π^3/(4V), providing a robust cross-check of the holographic dictionary. The generalized conifold case L^{p,q|q} is treated explicitly, illustrating the method and highlighting how gcd-induced degeneracies modify operator multiplicities while preserving charge ratios, with broader implications for extending this program to extended semiclassical strings and geometry-driven operator mappings.

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.

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

TL;DR

This work analyzes massless BPS geodesics in the toric Sasaki–Einstein spaces L^{p,q|r} within the AdS/CFT framework, establishing a precise correspondence with BPS mesons in the dual quiver gauge theories. By deriving an R-charge angle from the holomorphic three-form and mapping the toric GLSM data to quiver blocks, the authors connect geometric parameters to a-maximization data, validating the duality through central charges and volumes. They show that extremal geodesics correspond to four corner mesons, and that the a-maximization results precisely reproduce the geometric volumes via a = π^3/(4V), providing a robust cross-check of the holographic dictionary. The generalized conifold case L^{p,q|q} is treated explicitly, illustrating the method and highlighting how gcd-induced degeneracies modify operator multiplicities while preserving charge ratios, with broader implications for extending this program to extended semiclassical strings and geometry-driven operator mappings.

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.

Paper Structure

This paper contains 17 sections, 67 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Strings moving in the $L^{p,q|r}$ manifold
  3. A change of coordinates
  4. R-charge
  5. BPS geodesics
  6. From GLSM charges to quivers and chiral rings: $L^{p,q|r}$
  7. BPS mesons
  8. Resolving the strip: $L^{p, q|q}$
  9. Comparison with the geometry
  10. General case: $L^{p,q|r}$
  11. R-charges
  12. The volume of the manifold
  13. BPS operators and massless geodesics
  14. Conclusions
  15. Useful formulas
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Generic toric diagram with four edges. The related $(p,q)$-web is depicted.
  • Figure 2: Generic toric diagram with four edges. The intersection numbers are computed.
  • Figure 3: From fig.\ref{['pqweb']} we extract the multiplicities of the bi-fundamental fields. We define $q=as-bp$ and $r=p+q-s$.
  • Figure 4: Vertices (or nodes) appearing in the toric representation of the quiver.
  • Figure 5: Building blocks of the toric representation of the quiver.
  • ...and 3 more figures