Comments on the non-conformal gauge theories dual to Ypq manifolds

TL;DR

Brini and Forcella analyze the IR dynamics of the full class of toric quiver gauge theories dual to $Y^{p,q}$ and related $L^{a,b,c}$ geometries using dimer techniques. They demonstrate that nonperturbative $ADS$ terms generically lift baryonic flat directions to infinity, leading to runaway behavior rather than stable vacua, and they illustrate this with explicit runs in $Y^{2,1}$ and Del Pezzo examples, extending the picture to broader toric families. The work clarifies how cascades, rank assignments, and ADS contributions shape the IR, and discusses implications for the gravity dual and potential metastable vacua, while noting that Kähler potential effects could alter stabilization. Overall, the findings suggest a robust runaway mechanism across a wide swath of toric quivers, with significant implications for gauge/gravity duality in nonconformal settings.

Abstract

We study the infrared behavior of the entire class of Y(p,q) quiver gauge theories. The dimer technology is exploited to discuss the duality cascades and support the general belief about a runaway behavior for the whole family. We argue that a baryonic classically flat direction is pushed to infinity by the appearance of ADS-like terms in the effective superpotential. We also study in some examples the IR regime for the L(a,b,c) class showing that the same situation might be reproduced in this more general case as well.

Figures (27)

• Figure 1: (A) The toric diagram of $Y^{p,q}$ manifolds. (B) The $(p,q)$-wed diagram of $Y^{p,q}$ manifolds. In the figure we show the specific case of $Y^{5,2}$
• Figure 2: The generic dimer for $Y^{p,q}$
• Figure 3: The four different families of gauge factors that give the four different beta functions in the theory.
• Figure 4: The tiling orientation.
• Figure 5: Seiberg duality in the brane tiling