Tetrahedron Instantons

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes flat spacetime with proper constant $B$-field. Physically they capture instantons on $\mathbb{C}^{3}$ the presence most general real codimension-two supersymmetric defects. Moreover, we construct as particular solutions instanton equations noncommutative field theory. analyze moduli space discuss geometric interpretations. compute partition function both via equivariant localization elliptic genus worldvolume D$7$-branes, obtaining same result. The lies between higher-rank Donaldson-Thomas invariants magnificent four model, is conjectured to mother all functions. Finally, show that admits free representation, suggesting existence novel kind symmetry acts cohomology spaces instantons.