New atomic building blocks for five-dimensional quantum field theories

Using M-theory geometric engineering, the authors construct a new family of 5d superconformal field theories called trinions and tetraons — multi-legged junctions that generalize the simpler two-leg bifundamental building blocks used in linear quiver theories. These objects carry D-type flavor symmetry and, when fused, produce non-linear quiver theories with unexpected enhancements of instanton symmetry. The underlying geometry is often non-toric and cannot be expressed as a complete intersection, pushing beyond standard toolkits. A no-go result rules out analogous E-type trinions and tetraons, drawing a firm boundary on this classification program.