Hidden Exceptional Global Symmetries in 4d CFTs

TL;DR

This work uncovers hidden ${E_n}$ global symmetries in 4d ${\cal N}=1$ quiver gauge theories from D3-branes on complex cones over del Pezzo surfaces by mapping bifundamentals to geometric divisors. The authors develop a unified framework that organizes matter into ${E_n}$ representations, derives superpotentials from ${E_n}$ invariants, and explains partial representations for non-toric cases, with Higgsing corresponding to geometric blow-downs. Seiberg duality is shown to preserve the ${E_n}$ structure, with mesons completing representations across dual phases. The paper also provides a dual geometric-algebraic approach to count dibaryons and verifies AdS/CFT predictions, extending the analysis to ${dP_7}$ and ${dP_8}$ via maximal subgroups and offering a comprehensive link between geometry, symmetry, and holography.

Abstract

We study four dimensional N=1 gauge theories that arise on the worldvolume of D3-branes probing complex cones over del Pezzo surfaces. Global symmetries of the gauge theories are made explicit by using a correspondence between bifundamental fields in the quivers and divisors in the underlying geometry. These global symmetries are hidden, being unbroken when all inverse gauge couplings of the quiver theory vanish. In the broken phase, for finite gauge couplings, only the Cartan subalgebra is manifest as a global symmetry. Superpotentials for these models are constructed using global symmetry invariants as their building blocks. Higgsings connecting theories for different del Pezzos are immediately identified by performing the appropriate higgsing of the global symmetry groups. The symmetric properties of the quivers are also exploited to count the first few dibaryon operators in the gauge theories, matching their enumeration in the AdS duals.

Figures (31)

• Figure 1: Quiver diagram for Model I of $dP_2$.
• Figure 2: Quiver diagram for Model II of $dP_2$.
• Figure 3: Quiver diagram for Model I of $dP_3$.
• Figure 4: Quiver diagram for Model II of $dP_3$.
• Figure 5: Quiver diagram for Model III of $dP_3$.