Conformal Manifolds for the Conifold and other Toric Field Theories

TL;DR

This work identifies and characterizes the conformal manifolds of 4D $N=1$ quiver gauge theories arising from D3 branes at toric Calabi--Yau singularities. The authors show that the conifold has a five complex–dimensional conformal manifold, while generic $Y^{p,q}$ theories have a three complex–dimensional one, with a universal $\beta$-deformation present for all toric Calabi--Yau geometries; other directions correspond to fluxes and gauge-coupling variations and are tied to dual gravity descriptions. They map marginal deformations to chiral operators and fluxes, analyze moduli spaces of vacua, and study Higgsed IR theories, including special RG flows such as $Y^{1,1}\to Y^{1,0}$ and $Y^{2,2}\to Y^{2,0}$. The results clarify which deformations are exactly marginal vs marginally irrelevant, and they discuss implications for the gravity duals and duality cascades in toric quiver theories.

Abstract

In the space of couplings of the 4D N=1 gauge theory associated to D3 branes probing Calabi-Yau singularities, there is a manifold over which superconformal invariance is preserved. The AdS/CFT correspondence is valid precisely for this "conformal manifold". We identify the conformal manifold for all the Y^{p,q} toric singularities, paying special attention to the case of the conifold, Y^{1,0}. For a general Y^{p,q} the conformal manifold is three dimensional, while for the conifold it is five dimensional. There is always an exactly marginal deformation, analogous to the beta-deformation of N=4 SYM, which involves fluxes in the dual gravity description. This beta-deformation exists for any toric Calabi-Yau singularity.

Figures (2)

• Figure 1: The quiver diagram of the conifold field theory.
• Figure 2: The fixed line with vanishing superpotential.