Chiral flavors and M2-branes at toric CY4 singularities

TL;DR

The paper develops a comprehensive framework for 3d $\mathcal{N}=2$ quiver CS theories describing M2-branes on toric CY$_4$ cones with codimension-two degenerations, i.e., flavored theories arising from D6-branes. It combines a top-down M-theory reduction to IIA with D6-branes and a bottom-up flavored quiver approach, positing a holomorphic quantum relation $T^{(n)}T^{(-n)}=(\prod X_\alpha^{h_\alpha})^{|n|}$ for diagonal monopoles that fixes the flavored moduli space as a toric CY$_4$. The authors provide a general recipe to derive the flavored mesonic moduli space, show its toric nature via auxiliary A-theory brane tilings, and verify it across many explicit examples, including the $Q^{1,1,1}$ geometry. They also relate real and complex masses to geometric deformations of the IIA/M-theory background and discuss shifts in Chern-Simons levels induced by D6-branes. Overall, the work extends the AdS$_4$/CFT$_3$ dictionary to a broad class of flavored toric CY$_4$ singularities and offers concrete tools to engineer and study new holographic duals.

Abstract

We extend the stringy derivation of N=2 AdS4/CFT3 dualities to cases where the M-theory circle degenerates at complex codimension-two submanifolds of a toric conical CY4. The type IIA backgrounds include D6-branes, and the dual N=2 quiver gauge theories contain chiral flavors. We provide a general recipe to derive the geometric moduli space of flavored versions of Abelian toric quiver gauge theories. The CY4 cone is reproduced thanks to a non-trivial quantum F-term relation between diagonal monopole operators and bifundamental fields. We find new field theory duals to many geometries, including Q111.

Figures (16)

• Figure 1: Vertical projection from the 3d toric diagram of $Y_4$ to the 2d toric diagram of $Y_3$. The three aligned points give rise to two D6-branes.
• Figure 2: Deformation of the unflavored theory to construct the A-theory.
• Figure 3: Quivers for flavored SQED. Circles are gauge groups, squares are flavor groups. Colored arrows indicate bifundamental fields coupled to flavors via a superpotential term.
• Figure 4: Toric diagrams corresponding to some flavors for the $\mathbb{C}^3$ quiver.
• Figure 5: Toric diagrams of $\mathbb{C}^2\times \mathbb{C}^2/\mathbb{Z}_h$, for $h=3$.