Deformations of conformal theories and non-toric quiver gauge theories

TL;DR

The paper develops a framework to study deformations of conformal quiver gauge theories dual to Sasaki–Einstein backgrounds, constructing non-toric examples by relevant deformations of toric theories with isometries T$^2$ or T$^1$. It provides a consistent dictionary between mesonic spectra (via holomorphic functions and the Psi-map), baryonic data (via wrapped D3-branes), and geometric data (Reeb vector, volumes) through a-maximization and volume minimization, extending these ideas beyond toric cases. Detailed analyses of PdP$_4$/dP$_4$ and generalized A$_k$ conifolds demonstrate precise matches between central charges, R-charges, meson dimensions, and Sasaki–Einstein volumes, validating AdS/CFT predictions in non-toric settings. The work also develops tools to count holomorphic functions in non-toric cones, showing how to obtain $\mathcal{C}^*_{T^2}$ and $\mathcal{C}^*_{T^1}$ and connecting them to a-maximization through line- or plane-restricted volume minimization. Overall, the paper broadens the landscape of explicit AdS/CFT tests by bridging toric methods with controlled non-toric deformations and clarifying where volume extremization lives in these generalized contexts.

Abstract

We discuss several examples of non-toric quiver gauge theories dual to Sasaki-Einstein manifolds with U(1)^2 or U(1) isometry. We give a general method for constructing non-toric examples by adding relevant deformations to the toric case. For all examples, we are able to make a complete comparison between the prediction for R-charges based on geometry and on quantum field theory. We also give a general discussion of the spectrum of conformal dimensions for mesonic and baryonic operators for a generic quiver theory; in the toric case we make an explicit comparison between R-charges of mesons and baryons.

Figures (12)

• Figure 1: The toric diagram $P$ is a convex polygon in the plane with integer vertices obtained as the intersection of the toric fan $\mathcal{C}$ with the plane $z=1$.
• Figure 2: Quiver for $(P)dP_4$ theories.
• Figure 3: Dimer configuration and toric diagram for the toric $PdP_4$ theory.
• Figure 4: The multiplicities of holomorphic functions with fixed charge(s) over $(P)dP_4$ cones with a) isometry $T^2$, b) isometry $T^1$.
• Figure 5: Resolution of complex cone over $PdP_4$