5d SCFTs from $(E_n,E_m)$ Conformal Matter

Abstract

We determine 5d $\mathcal{N}=1$ SCFTs originating from 6d $(E_n,E_m)$ conformal matter theories with $n\neq m$ by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers.

Figures (12)

• Figure 1: Sketch of the singular Calabi-Yau 3-fold geometry $X_3$\ref{['eq:GeneralTateForm']}. Minimal singularities of Kodaira-type are supported along base divisors $u,v=0$ and enhance to a non-minimal singularity upon collision at the origin.
• Figure 2: The figure shows the intersection matrix \ref{['eq:IntMatrix']} for the rank 10 $(E_6,E_7)$ marginal geometry computed from the resolution \ref{['eq:blowups']}. The genus of a yellow/blue curves is formally $g=-1,-2$ respectively, while uncolored curves are of vanishing genus. The former are reducible while the latter are irreducible. Dashed lines denote negative intersection between curves indicating common components.
• Figure 3: Continuation of figure \ref{['fig:E6E7Raw1']}.
• Figure 4: The picture shows an $(E_6,E_7)$ marginal geometry related to the blowup sequence in \ref{['eq:blowups']}. Each diagram depicts the full set of generators for the Cox ring of the surface $S_k$. The curves $C_i$ in individual surfaces are distinct and enumerate excess generators not directly associated to section of the Calabi-Yau geometry. Their relation to the divisors of the Calabi-Yau restricted to $S_k$ is listed in \ref{['eq:DetailedRelations']}. Flavor curves of self-intersection $(-2)$ are colored green, manifest gluing curves are colored yellow and the remaining curves are colored white. Homologous curves are listed by '$/\,$'.
• Figure 5: $(E_6,E_7)$ marginal geometry. Figure \ref{['fig:FDE6E71']} continued.